Consider ideals II of the form [ I=(x12,…,xn2)+RLex(xixj)I=(x_1^2,dots , x_n^2)+operatorname {RLex}(x_ix_j) ] where RLex(xixj)operatorname {RLex}(x_ix_j) is the ideal generated by all the square-free monomials which are greater than or equal to xixjx_ix_j in the reverse lexicographic o
考虑形式为 I I 的理想[ I = ( x 1 2 , ... , x n 2 ) + RLex ( x i x j ) I=(x_1^2,dots , x_n^2)+operatorname {RLex}(x_ix_j) ]其中 RLex ( x i x j ) operatorname {RLex}(x_ix_j) 是由所有大于或等于 x i x j x_ix_j 的无平方单项式按相反的词序生成的理想。我们将确定有关 I I 的希尔伯特级数形状的一些有趣性质。利用林赛的定理[Proc. Amer. Math. Soc. 139 (2011), no.在 Phuong 和 Tran [Colloq. Math. 173 (2023), no.结果表明，对于artinian二次型理想的任何可能最小生成数，都存在这样一个理想，它由这么多单项式最小生成，并定义了一个具有强列夫谢茨性质的代数。
{"title":"The strong Lefschetz property for quadratic reverse lexicographic ideals","authors":"Filip Jonsson Kling","doi":"10.1090/bproc/234","DOIUrl":"https://doi.org/10.1090/bproc/234","url":null,"abstract":"<p>Consider ideals <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper I\">\u0000 <mml:semantics>\u0000 <mml:mi>I</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">I</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of the form <disp-formula content-type=\"math/mathml\">\u0000[\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper I equals left-parenthesis x 1 squared comma ellipsis comma x Subscript n Superscript 2 Baseline right-parenthesis plus upper R upper L e x left-parenthesis x Subscript i Baseline x Subscript j Baseline right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>I</mml:mi>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:msubsup>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msubsup>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mo>…</mml:mo>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:msubsup>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msubsup>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:mi>RLex</mml:mi>\u0000 <mml:mo></mml:mo>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mi>i</mml:mi>\u0000 </mml:msub>\u0000 <mml:msub>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mi>j</mml:mi>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">I=(x_1^2,dots , x_n^2)+operatorname {RLex}(x_ix_j)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000]\u0000</disp-formula> where <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R upper L e x left-parenthesis x Subscript i Baseline x Subscript j Baseline right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>RLex</mml:mi>\u0000 <mml:mo></mml:mo>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mi>i</mml:mi>\u0000 </mml:msub>\u0000 <mml:msub>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mi>j</mml:mi>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">operatorname {RLex}(x_ix_j)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is the ideal generated by all the square-free monomials which are greater than or equal to <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"x Subscript i Baseline x Subscript j\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mi>i</mml:mi>\u0000 </mml:msub>\u0000 <mml:msub>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mi>j</mml:mi>\u0000 </mml:msub>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">x_ix_j</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> in the reverse lexicographic o","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"90 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141657642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We give a new proof of the Gagliardo–Nirenberg and Sobolev inequalities based on the heat semigroup. Concerning the Gagliardo–Nirenberg inequality, we simplify the previous proof by relying only on the L p L^p - L q L^q estimate of the heat semigroup. For the Sobolev inequality, we consider another approach by using the heat semigroup and the Hardy inequality.
我们给出了基于热半群的 Gagliardo-Nirenberg 和 Sobolev 不等式的新证明。关于 Gagliardo-Nirenberg 不等式，我们仅依靠热半群的 L p L^p - L q L^q 估计值简化了之前的证明。对于索博廖夫不等式，我们考虑使用热半群和哈代不等式的另一种方法。
{"title":"A new proof of the Gagliardo–Nirenberg and Sobolev inequalities: Heat semigroup approach","authors":"Tohru Ozawa, Taiki Takeuchi","doi":"10.1090/bproc/211","DOIUrl":"https://doi.org/10.1090/bproc/211","url":null,"abstract":"We give a new proof of the Gagliardo–Nirenberg and Sobolev inequalities based on the heat semigroup. Concerning the Gagliardo–Nirenberg inequality, we simplify the previous proof by relying only on the \u0000\u0000 \u0000 \u0000 L\u0000 p\u0000 \u0000 L^p\u0000 \u0000\u0000-\u0000\u0000 \u0000 \u0000 L\u0000 q\u0000 \u0000 L^q\u0000 \u0000\u0000 estimate of the heat semigroup. For the Sobolev inequality, we consider another approach by using the heat semigroup and the Hardy inequality.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"113 16","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141657167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A Riemann surface equipped with its conformal hyperbolic metric is parabolic if and only if the geodesic flow on its unit tangent bundle is ergodic. Let X X be a Cantor tree or a blooming Cantor tree Riemann surface. Fix a geodesic pants decomposition of X X and call the boundary geodesics in the decomposition cuffs. Basmajian, Hakobyan, and Šarić proved that if the lengths of cuffs are rapidly converging to zero, then X X is parabolic. More recently, Šarić proved a slightly slower convergence of lengths of cuffs to zero implies X X is not parabolic. In this paper, we interpolate between the two rates of convergence of the cuffs to zero and find that these surfaces are not parabolic, thus completing the picture.
当且仅当其单位切线束上的大地流是遍历的时候，一个配备了共形双曲度量的黎曼曲面才是抛物面。设 X X 是康托树或开花康托树黎曼曲面。固定 X X 的测地线裤子分解，并称分解中的边界测地线为袖口。巴斯马坚、哈科比扬和沙里奇证明，如果袖口的长度迅速趋于零，那么 X X 是抛物面。最近，Šarić 证明了袖口长度收敛到零的速度稍慢意味着 X X 不是抛物线。在本文中，我们在袖口收敛到零的两个速率之间进行插值，发现这些曲面不是抛物面，从而完成了对问题的解释。
{"title":"Nonergodicity of the geodesic flow on a special class of Cantor tree surfaces","authors":"Michael Pandazis","doi":"10.1090/bproc/228","DOIUrl":"https://doi.org/10.1090/bproc/228","url":null,"abstract":"A Riemann surface equipped with its conformal hyperbolic metric is parabolic if and only if the geodesic flow on its unit tangent bundle is ergodic. Let \u0000\u0000 \u0000 X\u0000 X\u0000 \u0000\u0000 be a Cantor tree or a blooming Cantor tree Riemann surface. Fix a geodesic pants decomposition of \u0000\u0000 \u0000 X\u0000 X\u0000 \u0000\u0000 and call the boundary geodesics in the decomposition cuffs. Basmajian, Hakobyan, and Šarić proved that if the lengths of cuffs are rapidly converging to zero, then \u0000\u0000 \u0000 X\u0000 X\u0000 \u0000\u0000 is parabolic. More recently, Šarić proved a slightly slower convergence of lengths of cuffs to zero implies \u0000\u0000 \u0000 X\u0000 X\u0000 \u0000\u0000 is not parabolic. In this paper, we interpolate between the two rates of convergence of the cuffs to zero and find that these surfaces are not parabolic, thus completing the picture.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"65 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141693636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We obtain an explicit upper bound on the size of the coefficients of the elliptic modular polynomials ΦNPhi _N for any N≥1Ngeq 1. These polynomials vanish at pairs of jj-invariants of elliptic curves linked by cyclic isogenies of degree NN. The main term in the bound is asymptotically optimal as NN tends to infinity.
对于任意 N ≥ 1 Ngeq 1，我们得到了椭圆模态多项式 Φ N Phi _N 的系数大小的明确上限。这些多项式在椭圆曲线的 j j - 变项对上消失，这些变项通过 N N 度的循环同源关系相连。当 N N 趋于无穷大时，约束中的主项是渐近最优的。
{"title":"Explicit bounds on the coefficients of modular polynomials for the elliptic 𝑗-invariant","authors":"Florian Breuer, Fabien Pazuki","doi":"10.1090/bproc/179","DOIUrl":"https://doi.org/10.1090/bproc/179","url":null,"abstract":"<p>We obtain an explicit upper bound on the size of the coefficients of the elliptic modular polynomials <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Phi Subscript upper N\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi mathvariant=\"normal\">Φ</mml:mi>\u0000 <mml:mi>N</mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">Phi _N</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> for any <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N greater-than-or-equal-to 1\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>N</mml:mi>\u0000 <mml:mo>≥</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">Ngeq 1</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. These polynomials vanish at pairs of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"j\">\u0000 <mml:semantics>\u0000 <mml:mi>j</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">j</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-invariants of elliptic curves linked by cyclic isogenies of degree <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N\">\u0000 <mml:semantics>\u0000 <mml:mi>N</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">N</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. The main term in the bound is asymptotically optimal as <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N\">\u0000 <mml:semantics>\u0000 <mml:mi>N</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">N</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> tends to infinity.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"42 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141688840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Subject to given boundary data, nonexistence of solution to the one-dimensional Kirchhoff-like equation −M((a∗|u|q)(1))u(t)=λf(t,u(t)),0>t>1begin{equation*} -MBig (big (a*|u|^qbig )(1)Big )u(t)=lambda fbig (t,u(t)big ), 0>t>1 end{equation*}
在给定边界数据的条件下，一维基尔霍夫方程 - M ( ( a ∗ | u | q ) ( 1 ) u ( t ) = λ f ( t , u ( t ) 的解不存在） , 0 > t > 1 begin{equation*}-MBig (big (a*|u|^qbig )(1)Big )u(t)=lambda fbig (t,u(t)big ),0>t>1 end{equation*} 被考虑。特别是，在参数 λ lambda 上提供了一个条件，即对于每个 λ > λ 0 lambda > lambda _0 ，其中 λ 0 lambda _0 是根据初始数据定义的，边界值问题没有非奇异正解。
{"title":"Nonexistence of nontrivial solutions to Kirchhoff-like equations","authors":"Christopher Goodrich","doi":"10.1090/bproc/224","DOIUrl":"https://doi.org/10.1090/bproc/224","url":null,"abstract":"<p>Subject to given boundary data, nonexistence of solution to the one-dimensional Kirchhoff-like equation <disp-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"minus upper M left-parenthesis left-parenthesis a asterisk StartAbsoluteValue u EndAbsoluteValue Superscript q Baseline right-parenthesis left-parenthesis 1 right-parenthesis right-parenthesis u left-parenthesis t right-parenthesis equals lamda f left-parenthesis t comma u left-parenthesis t right-parenthesis right-parenthesis comma 0 greater-than t greater-than 1\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo>−</mml:mo>\u0000 <mml:mi>M</mml:mi>\u0000 <mml:mstyle scriptlevel=\"0\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo maxsize=\"1.623em\" minsize=\"1.623em\">(</mml:mo>\u0000 </mml:mrow>\u0000 </mml:mstyle>\u0000 <mml:mstyle scriptlevel=\"0\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">(</mml:mo>\u0000 </mml:mrow>\u0000 </mml:mstyle>\u0000 <mml:mi>a</mml:mi>\u0000 <mml:mo>∗</mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo stretchy=\"false\">|</mml:mo>\u0000 </mml:mrow>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:msup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo stretchy=\"false\">|</mml:mo>\u0000 </mml:mrow>\u0000 <mml:mi>q</mml:mi>\u0000 </mml:msup>\u0000 <mml:mstyle scriptlevel=\"0\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">)</mml:mo>\u0000 </mml:mrow>\u0000 </mml:mstyle>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mstyle scriptlevel=\"0\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo maxsize=\"1.623em\" minsize=\"1.623em\">)</mml:mo>\u0000 </mml:mrow>\u0000 </mml:mstyle>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mi>λ</mml:mi>\u0000 <mml:mi>f</mml:mi>\u0000 <mml:mstyle scriptlevel=\"0\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">(</mml:mo>\u0000 </mml:mrow>\u0000 </mml:mstyle>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mstyle scriptlevel=\"0\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">)</mml:mo>\u0000 </mml:mrow>\u0000 </mml:mstyle>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mtext> </mml:mtext>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo>></mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo>></mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">begin{equation*} -MBig (big (a*|u|^qbig )(1)Big )u(t)=lambda fbig (t,u(t)big ), 0>t>1 end{equation*}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</dis","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"87 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141699361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We provide new examples of étale extensions of Green functors by transferring classical examples of étale extensions to the equivariant setting. Our examples are Tambara functors, and we prove Green étaleness for them, which implies Tambara étaleness. We show that every C2C_2-Galois extensions of fields gives rise to an étale extension of C2C_2-Green functors. Here we associate the constant Tambara functor to the base field and the fix-Tambara functor to the extension. We also prove that all CnC_n-Kummer extensions give rise to étale extensions for arbitrary finite nn. Étale extensions of fields induce étale extension of GG-Green functors for any finite group GG by passing to the corresponding constant GG-Tambara functors.
我们通过将经典的等价扩展范例转移到等价环境，提供了格林函子等价扩展的新范例。我们的例子是坦巴拉函子，我们证明了它们的格林常数，这意味着坦巴拉常数。我们证明了场的每个 C 2 C_2 -伽罗瓦扩展都会引起 C 2 C_2 -格林函子的等价扩展。在这里，我们把恒定坦巴拉函子与基域联系起来，把固定坦巴拉函子与扩展联系起来。我们还证明，对于任意有限 n n，所有 C n C_n -库默扩展都会产生 étale 扩展。对于任意有限群 G G，通过传递到相应的恒定 G G -Tambara 函数，场的Étale扩展会引起 G G -Green 函数的Étale扩展。
{"title":"Examples of étale extensions of Green functors","authors":"A. Lindenstrauss, Birgit Richter, Foling Zou","doi":"10.1090/bproc/189","DOIUrl":"https://doi.org/10.1090/bproc/189","url":null,"abstract":"<p>We provide new examples of étale extensions of Green functors by transferring classical examples of étale extensions to the equivariant setting. Our examples are Tambara functors, and we prove Green étaleness for them, which implies Tambara étaleness. We show that every <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C 2\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>C</mml:mi>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">C_2</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-Galois extensions of fields gives rise to an étale extension of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C 2\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>C</mml:mi>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">C_2</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-Green functors. Here we associate the constant Tambara functor to the base field and the fix-Tambara functor to the extension. We also prove that all <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Subscript n\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>C</mml:mi>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">C_n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-Kummer extensions give rise to étale extensions for arbitrary finite <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n\">\u0000 <mml:semantics>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. Étale extensions of fields induce étale extension of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-Green functors for any finite group <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> by passing to the corresponding constant <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-Tambara functors.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"74 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141714856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We show that the characters of slrmathfrak {sl}_r versions of the (1,p)(1,p) singlet and the (1,p)(1,p) triplet vertex operator algebras arise as limits of appropriately coloured slrmathfrak {sl}_r Jones invariants of certain torus links.
我们证明了 s l r mathfrak {sl}_r 版本的 ( 1 , p ) (1,p) 单顶算子和 ( 1 , p ) (1,p) 三顶算子代数的特征是作为某些环链的适当颜色 s l r mathfrak {sl}_r 琼斯不变式的极限出现的。
{"title":"Characters of logarithmic vertex operator algebras and coloured invariants of torus links","authors":"S. Kanade","doi":"10.1090/bproc/223","DOIUrl":"https://doi.org/10.1090/bproc/223","url":null,"abstract":"<p>We show that the characters of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"German s German l Subscript r\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"fraktur\">s</mml:mi>\u0000 <mml:mi mathvariant=\"fraktur\">l</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>r</mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathfrak {sl}_r</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> versions of the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis 1 comma p right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">(1,p)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> singlet and the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis 1 comma p right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">(1,p)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> triplet vertex operator algebras arise as limits of appropriately coloured <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"German s German l Subscript r\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"fraktur\">s</mml:mi>\u0000 <mml:mi mathvariant=\"fraktur\">l</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>r</mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathfrak {sl}_r</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> Jones invariants of certain torus links.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"2 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141266169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We construct holomorphic support functions for smooth weakly pseudoconvex hypersurfaces with Levi form of constant rank. These are then applied to show that formal holomorphic curves which are tangential to infinite order to such a hypersurface must be formally contained in its Levi foliation. As a consequence, we obtain a holomorphic deformation theorem for nowhere smooth CR maps into smooth pseudoconvex hypersurfaces with one-dimensional Levi foliation, strengthening a very general result of Lamel and Mir about formal deformations in this particular case.
我们为具有恒等阶 Levi 形式的光滑弱假凸超曲面构建了全形支撑函数。然后，我们应用这些函数来证明，与这样的超曲面无限阶相切的形式全形曲线必须形式上包含在它的 Levi 折叠中。因此，我们得到了无处光滑 CR 映射到具有一维 Levi 叶形的光滑伪凸超曲面的全形变换定理，加强了 Lamel 和 Mir 关于这种特殊情况下形式变形的一个非常普遍的结果。
{"title":"Holomorphic support functions for uniformly pseudoconvex hypersurfaces, with an application to CR maps","authors":"Josef Greilhuber","doi":"10.1090/bproc/222","DOIUrl":"https://doi.org/10.1090/bproc/222","url":null,"abstract":"We construct holomorphic support functions for smooth weakly pseudoconvex hypersurfaces with Levi form of constant rank. These are then applied to show that formal holomorphic curves which are tangential to infinite order to such a hypersurface must be formally contained in its Levi foliation. As a consequence, we obtain a holomorphic deformation theorem for nowhere smooth CR maps into smooth pseudoconvex hypersurfaces with one-dimensional Levi foliation, strengthening a very general result of Lamel and Mir about formal deformations in this particular case.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141267710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stefan Glock, Felix Joos, Jaehoon Kim, Marcus Kühn, Lyuben Lichev, Oleg Pikhurko
Let f(r)(n;s,k)f^{(r)}(n;s,k) be the maximum number of edges of an rr-uniform hypergraph on nn vertices not containing a subgraph with kk edges and at most ss vertices. In 1973, Brown, Erdős, and Sós conjectured that the limit limn→∞n−2
设 f ( r ) ( n ; s , k ) f^{(r)}(n;s,k) 是一个 n n 个顶点上的 r r 个均匀超图的最大边数，该超图不包含一个有 k k 条边、最多有 s s 个顶点的子图。1973 年，布朗、厄尔多斯和索斯猜想，极限 lim n → ∞ n - 2 f ( 3 ) ( n ; k + 2 , k ) （开始{公式*}）。lim _{nto infty } n^{-2} f^{(3)}(n;k+2,k) end{equation*} 对于所有 k k 都存在，并且在 k = 2 k=2 时得到了证实。最近，格洛克证明了 k = 3 k=3 的情况。我们通过证明 f ( 3 ) ( n ; 6 , 4 ) = ( 7 36 + o ( 1 ) ) n 2 f^{(3)}(n;6,4)=left (frac {7}{36}+o(1)right )n^2 as n → ∞ nto infty 来解决下一个未知情况，即 k = 4 k=4 。更一般地说，对于所有 k∈ { 3 , 4 } kin {3,4} ，r ≥ 3rge ≥ 3 rge ≥ 3 rge ≥ 3 rge 。 , r ≥ 3 rge 3 and t ∈ [ 2 , r - 1 ] tin [2,r-1] , 我们计算极限值 lim n → ∞ n - t f ( r ) ( n ; k (
{"title":"On the (6,4)-problem of Brown, Erdős, and Sós","authors":"Stefan Glock, Felix Joos, Jaehoon Kim, Marcus Kühn, Lyuben Lichev, Oleg Pikhurko","doi":"10.1090/bproc/170","DOIUrl":"https://doi.org/10.1090/bproc/170","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f Superscript left-parenthesis r right-parenthesis Baseline left-parenthesis n semicolon s comma k right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msup>\u0000 <mml:mi>f</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>r</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 </mml:msup>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>;</mml:mo>\u0000 <mml:mi>s</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>k</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">f^{(r)}(n;s,k)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> be the maximum number of edges of an <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"r\">\u0000 <mml:semantics>\u0000 <mml:mi>r</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">r</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-uniform hypergraph on <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n\">\u0000 <mml:semantics>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> vertices not containing a subgraph with <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\">\u0000 <mml:semantics>\u0000 <mml:mi>k</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">k</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> edges and at most <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"s\">\u0000 <mml:semantics>\u0000 <mml:mi>s</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">s</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> vertices. In 1973, Brown, Erdős, and Sós conjectured that the limit <disp-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"limit Underscript n right-arrow normal infinity Endscripts n Superscript negative 2 f Superscript left-parenthesis 3 right-parenthesis Baseline left-parenthesis n semicolon k plus 2 comma k right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:munder>\u0000 <mml:mo movablelimits=\"true\" form=\"prefix\">lim</mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo stretchy=\"false\">→</mml:mo>\u0000 <mml:mi mathvariant=\"normal\">∞</mml:mi>\u0000 </mml:mrow>\u0000 </mml:munder>\u0000 <mml:msup>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo>−</mml:mo>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:mrow>\u0000 </mml:msup>\u0000 <mml:msup>\u0000 <mml:mi","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"87 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141267856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A useful result of H. Rosenthal and J. Bourgain states that, given a Banach space XX, an operator T:L1[0,1]→XT:L_1[0,1]to X is completely continuous if and only if its composition with the natural inclusion i∞:L∞[0,1]→L1[0,1]i_infty :L_infty [0,1] to L_1[0,1] is compact. We extend this result to multilinear mappings on products of L1[0,1]L_1[0,1]
罗森塔尔（H. Rosenthal）和布尔甘（J. Bourgain）的一个有用结果指出，给定一个巴拿赫空间 X X，当且仅当一个算子 T : L 1 [ 0 , 1 ] → X T:L_1[0,1]to X 与自然包含 i ∞ : L ∞ [ 0 , 1 ] → L 1 [ 0 , 1 ] i_infty :L_infty [0,1] to L_1[0,1] 的组合是紧凑的时候，这个算子 T 才是完全连续的。我们将这一结果扩展到 L 1 [ 0 , 1 ] L_1[0 , 1] 空间乘积上的多线性变换，并考虑与自然包含 i : C [ 0 , 1 ] → L 1 [ 0 , 1 ] i:C[0 , 1]to L_1[0 , 1] 的组合。我们证明，L 1 [ 0 , 1 ] L_1[0,1]空间乘积上的多线性映射是完全连续的，当且仅当其相关的多度量具有相对规范紧凑的范围。
{"title":"Completely continuous multilinear mappings on 𝐿₁","authors":"Raffaella Cilia, Joaquín Gutiérrez","doi":"10.1090/bproc/213","DOIUrl":"https://doi.org/10.1090/bproc/213","url":null,"abstract":"<p>A useful result of H. Rosenthal and J. Bourgain states that, given a Banach space <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\">\u0000 <mml:semantics>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">X</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, an operator <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper T colon upper L 1 left-bracket 0 comma 1 right-bracket right-arrow upper X\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>T</mml:mi>\u0000 <mml:mo>:</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">]</mml:mo>\u0000 <mml:mo stretchy=\"false\">→</mml:mo>\u0000 <mml:mi>X</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">T:L_1[0,1]to X</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is completely continuous if and only if its composition with the natural inclusion <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"i Subscript normal infinity Baseline colon upper L Subscript normal infinity Baseline left-bracket 0 comma 1 right-bracket right-arrow upper L 1 left-bracket 0 comma 1 right-bracket\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mi>i</mml:mi>\u0000 <mml:mi mathvariant=\"normal\">∞</mml:mi>\u0000 </mml:msub>\u0000 <mml:mo>:</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:mi mathvariant=\"normal\">∞</mml:mi>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">]</mml:mo>\u0000 <mml:mo stretchy=\"false\">→</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">]</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">i_infty :L_infty [0,1] to L_1[0,1]</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is compact. We extend this result to multilinear mappings on products of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L 1 left-bracket 0 comma 1 right-bracket\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">]</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">L_1[0,1]</mml:annotation>\u0000 </mml:seman","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"136 38","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140976877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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