We develop the theory of trace modules up to isomorphism and explore the relationship between preenveloping classes of modules and the property of being a trace module, guided by the question of whether a given module is trace in a given preenvelope. As a consequence we identify new examples of trace ideals and trace modules, and characterize several classes of rings with a focus on the Gorenstein and regular properties.
{"title":"The trace property in preenveloping classes","authors":"H. Lindo, Peder Thompson","doi":"10.1090/bproc/157","DOIUrl":"https://doi.org/10.1090/bproc/157","url":null,"abstract":"We develop the theory of trace modules up to isomorphism and explore the relationship between preenveloping classes of modules and the property of being a trace module, guided by the question of whether a given module is trace in a given preenvelope. As a consequence we identify new examples of trace ideals and trace modules, and characterize several classes of rings with a focus on the Gorenstein and regular properties.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133410217","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}
In this paper, we give a graphical version of the Ekeland’s variational principle (EVP) for equilibrium problems on weighted graphs. This version generalizes and includes other equilibrium types of EVP such as optimization, saddle point, fixed point and variational inequality ones. We also weaken the conditions on the class of bifunctions for which the variational principle holds by replacing the strong triangle inequality property by a below approximation of the bifunctions.
{"title":"Graphical Ekeland’s principle for equilibrium problems","authors":"M. Alfuraidan, M. Khamsi","doi":"10.1090/bproc/117","DOIUrl":"https://doi.org/10.1090/bproc/117","url":null,"abstract":"In this paper, we give a graphical version of the Ekeland’s variational principle (EVP) for equilibrium problems on weighted graphs. This version generalizes and includes other equilibrium types of EVP such as optimization, saddle point, fixed point and variational inequality ones. We also weaken the conditions on the class of bifunctions for which the variational principle holds by replacing the strong triangle inequality property by a below approximation of the bifunctions.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"330 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133569054","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}
The Neretin group Nd,kmathcal {N}_{d, k} is the totally disconnected locally compact group consisting of almost automorphisms of the tree Td,kmathcal {T}_{d, k}. This group has a distinguished open subgroup Od,kmathcal {O}_{d, k}. We prove that this open subgroup is not of type I. This gives an alternative proof of the recent result of P.-E. Caprace, A. Le Boudec and N. Matte Bon which states that the Neretin group is not of type I, and answers their question whether Od,kmathcal {O}_{d, k} is of type I or not.
Neretin群N d, k mathcal {N}_{d, k}是由树T d, k mathcal {T}_{d, k}的几乎自同构组成的完全不连通的局部紧群。这个群有一个开放的子群O d, k mathcal {O}_{d, k}。我们证明了这个开放子群不是i型的，给出了p - e最近结果的另一种证明。Caprace, A. Le Boudec和N. Matte Bon指出Neretin群不是I型，并回答了他们的问题O d, k mathcal {O}_{d, k}是否属于I型。
{"title":"On the type of the von Neumann algebra of an open subgroup of the Neretin group","authors":"Ryoya Arimoto","doi":"10.1090/bproc/133","DOIUrl":"https://doi.org/10.1090/bproc/133","url":null,"abstract":"<p>The Neretin group <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper N Subscript d comma k\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">N</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>d</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>k</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathcal {N}_{d, k}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is the totally disconnected locally compact group consisting of almost automorphisms of the tree <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper T Subscript d comma k\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">T</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>d</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>k</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathcal {T}_{d, k}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. This group has a distinguished open subgroup <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper O Subscript d comma k\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">O</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>d</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>k</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathcal {O}_{d, k}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. We prove that this open subgroup is not of type I. This gives an alternative proof of the recent result of P.-E. Caprace, A. Le Boudec and N. Matte Bon which states that the Neretin group is not of type I, and answers their question whether <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper O Subscript d comma k\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">O</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>d</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>k</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathcal {O}_{d, k}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is of type I or not.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"279 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114157370","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 integrable PT-symmetric nonlocal reductions for an integrable hierarchy associated with the special orthogonal Lie algebra so(3,R)operatorname {so}(3,mathbb {R}). The resulting typical nonlocal integrable equations are integrable PT-symmetric nonlocal reverse-space, reverse-time and reverse-spacetime nonlinear Schrödinger equations associated with so(3,R)operatorname {so}(3,mathbb {R}).
Let KK be a number field with ring of integers OKmathcal O_{K}. We prove that if 33 does not divide [K:Q][K:mathbb Q] and 33 splits completely in KK, then there are no exceptional units in KK. In other words, there are no x,y
设K K是一个带有整数环的数字域O K 数学上的O_{K}。证明了如果33不能除[K: Q] [K:mathbb Q]且33在K K中完全分裂，则K K中不存在例外单位。换句话说，不存在x, y∈O K x x, y 在数学的O_{K}^{times}中x + y = 1 x + y = 1。初等p进证明的灵感来自于将Skolem-Chabauty-Coleman方法应用于射影线减三点的标量限制。将此结果应用于算术动力学中的一个问题，证明了如果f∈O K [x] f in mathcal O_{K}[x]在O K mathcal O_{K}中有一个长度为n n的有限循环轨道，则n∈{1,2,4}n in {1,2,4 }。
{"title":"There are no exceptional units in number fields of degree prime to 3 where 3 splits completely","authors":"N. Triantafillou","doi":"10.1090/bproc/80","DOIUrl":"https://doi.org/10.1090/bproc/80","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper 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> be a number field with ring of integers <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper O Subscript upper K\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">O</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>K</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathcal O_{K}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. We prove that if <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\">\u0000 <mml:semantics>\u0000 <mml:mn>3</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> does not divide <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-bracket upper K colon double-struck upper Q right-bracket\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mi>K</mml:mi>\u0000 <mml:mo>:</mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">Q</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mo stretchy=\"false\">]</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">[K:mathbb Q]</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> and <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\">\u0000 <mml:semantics>\u0000 <mml:mn>3</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> splits completely in <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper 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>, then there are no exceptional units in <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper 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>. In other words, there are no <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"x comma y element-of script upper O Subscript upper K Superscript times\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>y</mml:mi>\u0000 <mml","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129482553","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}
Let $G$ and $N$ be two finite groups of the same order. It is well-known that the existences of the following are equivalent: (a) a Hopf-Galois structure of type $N$ on any Galois $G$-extension; (b) a skew brace with additive group $N$ and multiplicative group $G$; (c) a regular subgroup isomorphic to $G$ in the holomorph of $N$. We shall say that $(G,N)$ is realizable when any of the above exists. Fixing $N$ to be a cyclic group, W. Rump (2019) has determined the groups $G$ for which $(G,N)$ is realizable. In this paper, fixing $G$ to be a cyclic group instead, we shall give a complete characterization of the groups $N$ for which $(G,N)$ is realizable.
{"title":"Hopf-Galois structures on cyclic extensions and skew braces with cyclic multiplicative group","authors":"C. Tsang","doi":"10.1090/bproc/138","DOIUrl":"https://doi.org/10.1090/bproc/138","url":null,"abstract":"Let $G$ and $N$ be two finite groups of the same order. It is well-known that the existences of the following are equivalent: (a) a Hopf-Galois structure of type $N$ on any Galois $G$-extension; (b) a skew brace with additive group $N$ and multiplicative group $G$; (c) a regular subgroup isomorphic to $G$ in the holomorph of $N$. We shall say that $(G,N)$ is realizable when any of the above exists. Fixing $N$ to be a cyclic group, W. Rump (2019) has determined the groups $G$ for which $(G,N)$ is realizable. In this paper, fixing $G$ to be a cyclic group instead, we shall give a complete characterization of the groups $N$ for which $(G,N)$ is realizable.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125227124","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 extend an old Ramsey Theoretic result which guarantees sums of terms from all partition regular linear systems in one cell of a partition of the set Nmathbb {N} of positive integers. We were motivated by a quite recent result which guarantees a sequence in one set with all of its sums two or more at a time in the complement of that set. A simple instance of our new results is the following. Let Pf(N)mathcal {P}_{f}(mathbb {N}) be the set of finite nonempty subsets of Nmathbb {N}. Given any finite partition R{mathcal R} of Nmathbb {N}, there exist
{"title":"Some new multi-cell Ramsey theoretic results","authors":"V. Bergelson, N. Hindman","doi":"10.1090/bproc/109","DOIUrl":"https://doi.org/10.1090/bproc/109","url":null,"abstract":"<p>We extend an old Ramsey Theoretic result which guarantees sums of terms from all partition regular linear systems in one cell of a partition of the set <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper N\">\u0000 <mml:semantics>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">N</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbb {N}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of positive integers. We were motivated by a quite recent result which guarantees a sequence in one set with all of its sums two or more at a time in the complement of that set. A simple instance of our new results is the following. Let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper P Subscript f Baseline left-parenthesis double-struck upper N right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">P</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>f</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">N</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathcal {P}_{f}(mathbb {N})</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> be the set of finite nonempty subsets of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper N\">\u0000 <mml:semantics>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">N</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbb {N}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. Given any finite partition <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper R\">\u0000 <mml:semantics>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">R</mml:mi>\u0000 </mml:mrow>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">{mathcal R}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper N\">\u0000 <mml:semantics>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">N</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbb {N}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, there exist <inline-formula content-type=\"math/mathm","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125455460","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}
This article studies the properties of positive definite, radial functions on free groups following the work of Haagerup and Knudby [Proc. Amer. Math. Soc. 143 (2015), pp. 1477–1489]. We obtain characterizations of radial functions with respect to the ℓ 2 ell ^{2} length on the free groups with infinite generators and the characterization of the positive definite, radial functions with respect to the ℓ p ell ^{p} length on the free real line with infinite generators for 0 > p ≤ 2 0 > p leq 2 . We obtain a Lévy-Khintchine formula for length-radial conditionally negative functions as well.
本文根据Haagerup和Knudby的工作，研究了自由群上的正定径向函数的性质。数学。Soc. 143 (2015)， pp. 1477-1489。我们得到了具有无限发生器的自由群上径向函数关于1,2 ell ^{2}长度的刻画，以及具有无限发生器的自由实线上关于1,2 ell ^{p}长度的正定径向函数对于0 > p≤2 > p leq 2的刻画。我们也得到了长度-径向条件负函数的l - khintchine公式。
{"title":"Characterization of positive definite, radial functions on free groups","authors":"C. Chuah, Zhen-Chuan Liu, Tao Mei","doi":"10.1090/bproc/158","DOIUrl":"https://doi.org/10.1090/bproc/158","url":null,"abstract":"This article studies the properties of positive definite, radial functions on free groups following the work of Haagerup and Knudby [Proc. Amer. Math. Soc. 143 (2015), pp. 1477–1489]. We obtain characterizations of radial functions with respect to the \u0000\u0000 \u0000 \u0000 ℓ\u0000 \u0000 2\u0000 \u0000 \u0000 ell ^{2}\u0000 \u0000\u0000 length on the free groups with infinite generators and the characterization of the positive definite, radial functions with respect to the \u0000\u0000 \u0000 \u0000 ℓ\u0000 \u0000 p\u0000 \u0000 \u0000 ell ^{p}\u0000 \u0000\u0000 length on the free real line with infinite generators for \u0000\u0000 \u0000 \u0000 0\u0000 >\u0000 p\u0000 ≤\u0000 2\u0000 \u0000 0 > p leq 2\u0000 \u0000\u0000. We obtain a Lévy-Khintchine formula for length-radial conditionally negative functions as well.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130516179","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 prove Strichartz estimates for the Schrödinger equation in Rnmathbb {R}^n, n≥3ngeq 3, with a Hamiltonian H=−Δ+μH = -Delta + mu. The perturbation μmu is a compactly supported measure in Rnmathbb {R}^n with dimension α>n−(1+1n−1
我们证明Strichartz薛定谔的保守for the equation in R n mathbb {R) ^ n , n≥3 geq 3里,用a哈密顿 H = −Δ + μH = -三角洲+ 你。《perturbationμ你是个compactly supported所拘束的 R n mathbb {R ^ n和维度的 α > n− ( 1 + 1 n − 1 ) 阿尔法> n - (1 + frac {1} {n-1})。《玩中级站是a local decay estimate in L 2 ( μ ) L ^ 2 ( mu)一起的两人薛定谔(free and perturbed进化。
{"title":"Strichartz estimates for the Schrödinger equation with a measure-valued potential","authors":"M. Erdogan, M. Goldberg, William Green","doi":"10.1090/bproc/79","DOIUrl":"https://doi.org/10.1090/bproc/79","url":null,"abstract":"<p>We prove Strichartz estimates for the Schrödinger equation in <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper R Superscript n\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">R</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbb {R}^n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n greater-than-or-equal-to 3\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>≥<!-- ≥ --></mml:mo>\u0000 <mml:mn>3</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">ngeq 3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, with a Hamiltonian <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H equals negative normal upper Delta plus mu\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>H</mml:mi>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mo>−<!-- − --></mml:mo>\u0000 <mml:mi mathvariant=\"normal\">Δ<!-- Δ --></mml:mi>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:mi>μ<!-- μ --></mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">H = -Delta + mu</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. The perturbation <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"mu\">\u0000 <mml:semantics>\u0000 <mml:mi>μ<!-- μ --></mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">mu</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is a compactly supported measure in <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper R Superscript n\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">R</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbb {R}^n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> with dimension <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"alpha greater-than n minus left-parenthesis 1 plus StartFraction 1 Over n minus 1 EndFraction right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>α<!-- α --></mml:mi>\u0000 <mml:mo>></mml:mo>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>−<!-- − --></mml:mo>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:mfrac>\u0000 <mml:mn>1</mml:mn>\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:mfrac>\u0000 <mml:mo stretchy=","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124028572","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}
Using elementary hyperbolic geometry, we give an explicit formula for the contraction constant of the skinning map over moduli spaces of relatively acylindrical hyperbolic manifolds.
利用初等双曲几何，给出了相对非圆柱形双曲流形模空间上蒙皮映射的收缩常数的显式公式。
{"title":"Effective contraction of Skinning maps","authors":"Tommaso Cremaschi, L. D. Schiavo","doi":"10.1090/bproc/134","DOIUrl":"https://doi.org/10.1090/bproc/134","url":null,"abstract":"Using elementary hyperbolic geometry, we give an explicit formula for the contraction constant of the skinning map over moduli spaces of relatively acylindrical hyperbolic manifolds.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116153940","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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