We study the existence and uniqueness of strict solution for a general class of abstract explicit neutral equations with state-dependent delay. Some examples concerning explicit partial neutral differential equations with state dependent delay are presented.
{"title":"On explicit abstract neutral differential equations with state-dependent delay II","authors":"Eduardo Hernández","doi":"10.1090/proc/16861","DOIUrl":"https://doi.org/10.1090/proc/16861","url":null,"abstract":"<p>We study the existence and uniqueness of strict solution for a general class of abstract explicit neutral equations with state-dependent delay. Some examples concerning explicit partial neutral differential equations with state dependent delay are presented.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"64 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We give sufficient conditions for an expansive partially hyperbolic diffeomorphism with one-dimensional center to be (topologically) Anosov.
我们给出了具有一维中心的扩张性部分双曲衍射成为（拓扑）阿诺索夫的充分条件。
{"title":"Expansive partially hyperbolic diffeomorphisms with one-dimensional center","authors":"Martin Sambarino, José Vieitez","doi":"10.1090/proc/16845","DOIUrl":"https://doi.org/10.1090/proc/16845","url":null,"abstract":"<p>We give sufficient conditions for an expansive partially hyperbolic diffeomorphism with one-dimensional center to be (topologically) Anosov.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"135 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this note, we prove that the compactly supported mapping class group of a surface containing a genus 33 subsurface has no realization as a subgroup of the homeomorphism group. We also prove that for certain surfaces with order 66 symmetries, their mapping class groups have no realization as a subgroup of the homeomorphism group. Examples of such surfaces include the plane minus a Cantor set and the sphere minus a Cantor set.
{"title":"Non-realizability of some big mapping class groups","authors":"Lei Chen, Yan Mary He","doi":"10.1090/proc/16860","DOIUrl":"https://doi.org/10.1090/proc/16860","url":null,"abstract":"<p>In this note, we prove that the compactly supported mapping class group of a surface containing a genus <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\"> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding=\"application/x-tex\">3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> subsurface has no realization as a subgroup of the homeomorphism group. We also prove that for certain surfaces with order <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"6\"> <mml:semantics> <mml:mn>6</mml:mn> <mml:annotation encoding=\"application/x-tex\">6</mml:annotation> </mml:semantics> </mml:math> </inline-formula> symmetries, their mapping class groups have no realization as a subgroup of the homeomorphism group. Examples of such surfaces include the plane minus a Cantor set and the sphere minus a Cantor set.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"11 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
<p>Given a field <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding="application/x-tex">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, a rational function <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="phi element-of upper K left-parenthesis x right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>ϕ</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>K</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">phi in K(x)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and a point <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="b element-of double-struck upper P Superscript 1 Baseline left-parenthesis upper K right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>b</mml:mi> <mml:mo>∈</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant="double-struck">P</mml:mi> </mml:mrow> <mml:mn>1</mml:mn> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>K</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">b in mathbb {P}^1(K)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we study the extension <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K left-parenthesis phi Superscript negative normal infinity Baseline left-parenthesis b right-parenthesis right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>K</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mi>ϕ</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mi mathvariant="normal">∞</mml:mi> </mml:mrow> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>b</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">K(phi ^{-infty }(b))</mml:annotation> </mml:semantics> </mml:math> </inline-formula> generated by the union over <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding="application/x-tex">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of all solutions to <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="phi Superscript n Baseline left-parenthesis x right-parenthesis equals b"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>ϕ</mml:mi> <mml:mi>n</mml:mi> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>b</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">phi ^n(x) = b</mml:annotation> </mml:semantics> </mml:math> </inline-for
给定一个域 K K ，一个有理函数 ϕ ∈ K ( x ) phi in K(x) ，以及一个点 b ∈ P 1 ( K ) b in mathbb {P}^1(K) ，我们研究扩展 K ( ϕ - ∞ ( b ) ) K(phi ^{-infty }(b)) 由 ϕ n ( x ) = b phi ^n(x) = b 的所有解的 n n 的联合产生，其中 ϕ n phi ^n 是 ϕ phi 的第 n 个迭代。我们问当 K ( ϕ - ∞ ( b ) ) 的有限扩展时 K(phi ^{-infty }(b)) 可以包含某个 m ≥ 2 m geq 2 的所有 m m -power 单整根，并证明这发生在几个有理函数族中。一个有启发性的应用是理解当 K K 是 Q p mathbb {Q}_p 的有限扩展且 p p 除以 ϕ phi 的阶数时的高斜率滤波，尤其是当ϕ phi 是后极限（PCF）时。我们证明，对于新的迭代扩展族，例如那些由具有周期临界点的双临界有理函数给出的迭代扩展族，所有较高的斜切群都是无限的。我们还给出了迭代扩展的新例子，这些迭代扩展的子扩展满足更强的夯实理论条件，即算术剖分性。我们猜想，由 PCF 映射产生的每个迭代扩展都应该有一个具有这种更强性质的子扩展，这将给出 PCF 映射的森定理的动力学类似物。
{"title":"Roots of unity and higher ramification in iterated extensions","authors":"Spencer Hamblen, Rafe Jones","doi":"10.1090/proc/16825","DOIUrl":"https://doi.org/10.1090/proc/16825","url":null,"abstract":"<p>Given a field <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K\"> <mml:semantics> <mml:mi>K</mml:mi> <mml:annotation encoding=\"application/x-tex\">K</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, a rational function <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"phi element-of upper K left-parenthesis x right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>ϕ</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>K</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">phi in K(x)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and a point <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"b element-of double-struck upper P Superscript 1 Baseline left-parenthesis upper K right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>b</mml:mi> <mml:mo>∈</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">P</mml:mi> </mml:mrow> <mml:mn>1</mml:mn> </mml:msup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>K</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">b in mathbb {P}^1(K)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we study the extension <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K left-parenthesis phi Superscript negative normal infinity Baseline left-parenthesis b right-parenthesis right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>K</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msup> <mml:mi>ϕ</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mi mathvariant=\"normal\">∞</mml:mi> </mml:mrow> </mml:msup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>b</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">K(phi ^{-infty }(b))</mml:annotation> </mml:semantics> </mml:math> </inline-formula> generated by the union over <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n\"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding=\"application/x-tex\">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of all solutions to <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"phi Superscript n Baseline left-parenthesis x right-parenthesis equals b\"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>ϕ</mml:mi> <mml:mi>n</mml:mi> </mml:msup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>b</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">phi ^n(x) = b</mml:annotation> </mml:semantics> </mml:math> </inline-for","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"68 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a nonstationary random walk on a compact metrizable abelian group. Under a classical strict aperiodicity assumption we establish a weak-* convergence to the Haar measure, Ergodic Theorem and Large Deviation Type Estimate.
{"title":"Ergodic theorem for nonstationary random walks on compact abelian groups","authors":"Grigorii Monakov","doi":"10.1090/proc/16848","DOIUrl":"https://doi.org/10.1090/proc/16848","url":null,"abstract":"<p>We consider a nonstationary random walk on a compact metrizable abelian group. Under a classical strict aperiodicity assumption we establish a weak-* convergence to the Haar measure, Ergodic Theorem and Large Deviation Type Estimate.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"470 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study the global dynamics of epidemic network models with standard incidence or mass-action transmission mechanism, when the dispersal of either the susceptible or the infected people is controlled. The connectivity matrix of the model is not assumed to be symmetric. Our main technique to study the global dynamics is to construct novel Lyapunov type functions.
{"title":"Global dynamics of epidemic network models via construction of Lyapunov functions","authors":"Rachidi Salako, Yixiang Wu","doi":"10.1090/proc/16872","DOIUrl":"https://doi.org/10.1090/proc/16872","url":null,"abstract":"<p>In this paper, we study the global dynamics of epidemic network models with standard incidence or mass-action transmission mechanism, when the dispersal of either the susceptible or the infected people is controlled. The connectivity matrix of the model is not assumed to be symmetric. Our main technique to study the global dynamics is to construct novel Lyapunov type functions.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"21 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate polynomials that satisfy simultaneous orthogonality conditions with respect to several measures on the unit circle. We generalize the direct and inverse Szegő recurrence relations, identify the analogues of the Verblunsky coefficients, and prove the Christoffel–Darboux formula. These results should be viewed as the direct analogue of the nearest neighbour recurrence relations from the theory of multiple orthogonal polynomials on the real line.
{"title":"Szegő recurrence for multiple orthogonal polynomials on the unit circle","authors":"Rostyslav Kozhan, Marcus Vaktnäs","doi":"10.1090/proc/16811","DOIUrl":"https://doi.org/10.1090/proc/16811","url":null,"abstract":"<p>We investigate polynomials that satisfy simultaneous orthogonality conditions with respect to several measures on the unit circle. We generalize the direct and inverse Szegő recurrence relations, identify the analogues of the Verblunsky coefficients, and prove the Christoffel–Darboux formula. These results should be viewed as the direct analogue of the nearest neighbour recurrence relations from the theory of multiple orthogonal polynomials on the real line.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"46 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
<p>We establish a general framework for representability of a metric group on a (well-behaved) class of Banach spaces. More precisely, let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper G"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">G</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">mathcal {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a topological group, and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper A"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">A</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">mathcal {A}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> a unital symmetric <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Superscript asterisk"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:msup> <mml:annotation encoding="application/x-tex">C^*</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-subalgebra of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper U normal upper C left-parenthesis script upper G right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">U</mml:mi> <mml:mi mathvariant="normal">C</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mi mathvariant="script">G</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">mathrm {UC}(mathcal {G})</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the algebra of bounded uniformly continuous functions on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper G"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">G</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">mathcal {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Generalizing the notion of a stable metric, we study <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper A"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">A</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">mathcal {A}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-metrics <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="delta"> <mml:semantics> <mml:mi>δ<!-- δ --></mml:mi> <mml:annotation encoding="application/x-tex">delta</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, i.e., the function <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="delta left-parenthes
我们建立了在一类（良好的）巴拿赫空间上度量群的可表示性的一般框架。更确切地说，让 G mathcal {G} 是一个拓扑群，而 A mathcal {A} 是 U C ( G ) mathrm {UC}(mathcal {G}) 的有界对称 C ∗ C^* - 子代数，即 G mathcal {G} 上有界均匀连续函数的代数。从稳定度量的概念出发，我们研究 A mathcal {A} -metrics δ delta , 即、函数 δ ( e , ⋅ ) delta (e, cdot ) 属于 A mathcal {A}；在 A = W A P ( G ) mathcal {A}=Whskip -0.7mm Ahskip -0.2mm P(mathcal {G}) 的情况下，G 上弱几乎周期函数的代数 恢复稳定。如果 G G 的拓扑由左不变度量 d d 引起，我们证明当且仅当 d d 均匀等价于左不变 A mathcal {A} -度量时，A mathcal {A} 决定 G mathcal {G} 的拓扑。作为一个应用，我们证明了 C [ 0 , 1 ] 的加法群 C[0,1] 不可反身表示；这是 Megrelishvili [Topological transformation groups: selected topics, Elsevier, 2007, Question 6.7] 的一个新证明（这个问题早在 G [0 , 1] C[0,1] 中就由 Megrelishvili 解决了）。(费里和加林多 [Studia Math. 193 (2009), pp. 99-108] 用不同的方法解决了这个问题，后来雅科夫、贝伦斯坦和费里 [Math. Z. 267 (2011), pp.129-138] 对结果进行了推广）。现在让 G （mathcal {G}）是一个度量群，并假设 A ⊆ L U C ( G ) mathcal {A} subseteq mathrm {LUC}(mathcal {G}) , G （mathcal {G}）上有界左均匀连续函数的代数，是一个独元 C ∗ mathrm {LUC}(mathcal {G})。 是一个一元 C ∗ C^* -代数，它是 G 在 F （mathscr {F} 的成员）上的表示的系数的均匀闭包。 其中，F 是一类在 ℓ 2 ell _2 -direct sums 下封闭的巴拿赫空间。我们证明，当且仅当 G嵌入到 F 的一个成员的等几何群中时，A 才决定 G 的拓扑结构。 的等几何群中，并配备弱算子拓扑。作为应用，我们得到了单元可表示性和反射可表示性的特征。
{"title":"Representations of groups on Banach spaces","authors":"Stefano Ferri, Camilo Gómez, Matthias Neufang","doi":"10.1090/proc/16499","DOIUrl":"https://doi.org/10.1090/proc/16499","url":null,"abstract":"<p>We establish a general framework for representability of a metric group on a (well-behaved) class of Banach spaces. More precisely, let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper G\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"script\">G</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathcal {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a topological group, and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper A\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"script\">A</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathcal {A}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> a unital symmetric <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript asterisk\"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:msup> <mml:annotation encoding=\"application/x-tex\">C^*</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-subalgebra of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper U normal upper C left-parenthesis script upper G right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mi mathvariant=\"normal\">U</mml:mi> <mml:mi mathvariant=\"normal\">C</mml:mi> </mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mrow> <mml:mi mathvariant=\"script\">G</mml:mi> </mml:mrow> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathrm {UC}(mathcal {G})</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the algebra of bounded uniformly continuous functions on <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper G\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"script\">G</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathcal {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Generalizing the notion of a stable metric, we study <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper A\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"script\">A</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathcal {A}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-metrics <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"delta\"> <mml:semantics> <mml:mi>δ<!-- δ --></mml:mi> <mml:annotation encoding=\"application/x-tex\">delta</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, i.e., the function <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"delta left-parenthes","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"31 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
<p>We establish some <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Phi"> <mml:semantics> <mml:mi mathvariant="normal">Φ</mml:mi> <mml:annotation encoding="application/x-tex">Phi</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-moment inequalities for noncommutative differentially subordinate martingales. Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Phi"> <mml:semantics> <mml:mi mathvariant="normal">Φ</mml:mi> <mml:annotation encoding="application/x-tex">Phi</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-convex and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="q"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding="application/x-tex">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-concave Orlicz function with <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="1 greater-than p less-than-or-equal-to q greater-than 2"> <mml:semantics> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>></mml:mo> <mml:mi>p</mml:mi> <mml:mo>≤</mml:mo> <mml:mi>q</mml:mi> <mml:mo>></mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">1>pleq q>2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Suppose that <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="x"> <mml:semantics> <mml:mi>x</mml:mi> <mml:annotation encoding="application/x-tex">x</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="y"> <mml:semantics> <mml:mi>y</mml:mi> <mml:annotation encoding="application/x-tex">y</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are two self-adjoint martingales such that <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="y"> <mml:semantics> <mml:mi>y</mml:mi> <mml:annotation encoding="application/x-tex">y</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is weakly differentially subordinate to <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="x"> <mml:semantics> <mml:mi>x</mml:mi> <mml:annotation encoding="application/x-tex">x</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We show that, for <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" al
我们建立了一些非交换微分隶属马丁格的 Φ Phi -时刻不等式。设 Φ Phi 是一个 p p -凸且 q q -凹的 Orlicz 函数，其值为 1 > p ≤ q > 2 1>pleq q>2 。假设 x x 和 y y 是两个自相关的马丁格尔，且 y y 是 x x 的弱微分隶属。我们证明，对于 N≥0 Ngeq 0 , τ [ Φ ( | y N | ) ] ≤ c p , q τ [ Φ ( | x N | ) ] , begin{equation*}.tau big [Phi (|y_N|)big ]leq c_{p,q}tau big [Phi (|x_N|)big ], end{equation*} 其中常数 c p , q c_{p,q} 是 p = q p=q 时的最佳阶。本文还得到了非交换微分隶属马丁格的平方函数的 Φ Phi -动量估计。我们的方法提供了非交换 Φ Phi -矩 Burkholder-Gundy 不等式和 Burkholder 不等式的构造证明。
{"title":"Φ-moment inequalities for noncommutative differentially subordinate martingales","authors":"Yong Jiao, Mohammad Moslehian, Lian Wu, Yahui Zuo","doi":"10.1090/proc/16847","DOIUrl":"https://doi.org/10.1090/proc/16847","url":null,"abstract":"<p>We establish some <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Phi\"> <mml:semantics> <mml:mi mathvariant=\"normal\">Φ</mml:mi> <mml:annotation encoding=\"application/x-tex\">Phi</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-moment inequalities for noncommutative differentially subordinate martingales. Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Phi\"> <mml:semantics> <mml:mi mathvariant=\"normal\">Φ</mml:mi> <mml:annotation encoding=\"application/x-tex\">Phi</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\"application/x-tex\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-convex and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q\"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding=\"application/x-tex\">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-concave Orlicz function with <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"1 greater-than p less-than-or-equal-to q greater-than 2\"> <mml:semantics> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>></mml:mo> <mml:mi>p</mml:mi> <mml:mo>≤</mml:mo> <mml:mi>q</mml:mi> <mml:mo>></mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">1>pleq q>2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Suppose that <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"x\"> <mml:semantics> <mml:mi>x</mml:mi> <mml:annotation encoding=\"application/x-tex\">x</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"y\"> <mml:semantics> <mml:mi>y</mml:mi> <mml:annotation encoding=\"application/x-tex\">y</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are two self-adjoint martingales such that <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"y\"> <mml:semantics> <mml:mi>y</mml:mi> <mml:annotation encoding=\"application/x-tex\">y</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is weakly differentially subordinate to <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"x\"> <mml:semantics> <mml:mi>x</mml:mi> <mml:annotation encoding=\"application/x-tex\">x</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We show that, for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" al","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"27 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141516638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study a class of kk-Hessian equations, we can deduce an Obata-type formula and a Liouville-type theorem by integration by parts.
本文研究了一类 k k -Hessian 方程，通过分式积分，我们可以推导出 Obata 型公式和 Liouville 型定理。
{"title":"An Obata-type formula and the Liouville-type theorem for a class of K-Hessian equations on the sphere","authors":"Shujun Shi, Peihe Wang, Tian Wu, Hua Zhu","doi":"10.1090/proc/16857","DOIUrl":"https://doi.org/10.1090/proc/16857","url":null,"abstract":"<p>In this paper, we study a class of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\"> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=\"application/x-tex\">k</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Hessian equations, we can deduce an Obata-type formula and a Liouville-type theorem by integration by parts.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"19 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141530933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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