Proceedings of the American Mathematical Society最新文献

{"title":"Lie semisimple algebras of derivations and varieties of PI-algebras with almost polynomial growth","authors":"Sebastiano Argenti","doi":"10.1090/proc/16896","DOIUrl":"https://doi.org/10.1090/proc/16896","url":null,"abstract":"<p>We consider associative algebras with an action by derivations by some finite dimensional and semisimple Lie algebra. We prove that if a differential variety has almost polynomial growth, then it is generated by one of the algebras <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper U upper T 2 left-parenthesis upper W Subscript lamda Baseline right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>U</mml:mi> <mml:msub> <mml:mi>T</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>λ</mml:mi> </mml:msub> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">UT_2(W_lambda )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> or <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E n d left-parenthesis upper W Subscript mu Baseline right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mi>n</mml:mi> <mml:mi>d</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">End(W_mu )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for some integral dominant weight <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"lamda comma mu\"> <mml:semantics> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>μ</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">lambda ,mu</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"mu not-equals 0\"> <mml:semantics> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mo>≠</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mu neq 0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In the special case <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L equals German s German l Subscript 2\"> <mml:semantics> <mml:mrow> <mml:mi>L</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mrow> <mml:mi mathvariant=\"fraktur\">s</mml:mi> <mml:mi mathvariant=\"fraktur\">l</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">L=mathfrak {sl}_2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> we prove that this is a sufficient condition too.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"214 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872377","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}

{"title":"SAT actions of discrete quantum groups and minimal injective extensions of their von Neumann algebras","authors":"Mehrdad Kalantar, Fatemeh Khosravi, Mohammad Moakhar","doi":"10.1090/proc/16882","DOIUrl":"https://doi.org/10.1090/proc/16882","url":null,"abstract":"<p>We introduce a natural generalization of the notion of strongly approximately transitive (SAT) states for actions of locally compact quantum groups. In the case of discrete quantum groups of Kac type, we show that the existence of unique stationary SAT states entails rigidity results concerning injective extensions of quantum group von Neumann algebras.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"27 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197123","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}

{"title":"A note on almalgamated free products","authors":"Qihui Li, Don Hadwin, Junhao Shen","doi":"10.1090/proc/16791","DOIUrl":"https://doi.org/10.1090/proc/16791","url":null,"abstract":"<p>We prove a general result concerning properties preserved under certain amalgamated free products.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"14 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151831","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}

{"title":"Radon–Nikodým property and Lau’s conjecture","authors":"Andrzej Wiśnicki","doi":"10.1090/proc/16884","DOIUrl":"https://doi.org/10.1090/proc/16884","url":null,"abstract":"<p>There is a long-standing problem, posed by A.T.-M. Lau [<italic>Fixed point theory and its applications</italic>, Academic Press, New York-London, 1976, pp. 121–129], whether left amenability is sufficient to ensure the existence of a common fixed point for every jointly weak<inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"Superscript asterisk\"> <mml:semantics> <mml:msup> <mml:mi/> <mml:mrow> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">^{ast }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> continuous nonexpansive semigroup action on a nonempty weak<inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"Superscript asterisk\"> <mml:semantics> <mml:msup> <mml:mi/> <mml:mrow> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">^{ast }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> compact convex set in a dual Banach space. In this note we discuss the current status of this problem and give a partial solution in the case of weak<inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"Superscript asterisk\"> <mml:semantics> <mml:msup> <mml:mi/> <mml:mrow> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">^{ast }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> compact convex sets with the Radon–Nikodým property.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"68 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872178","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}

{"title":"Hyperfiniteness for group actions on trees","authors":"Srivatsav Kunnawalkam Elayavalli, Koichi Oyakawa, Forte Shinko, Pieter Spaas","doi":"10.1090/proc/16851","DOIUrl":"https://doi.org/10.1090/proc/16851","url":null,"abstract":"<p>We identify natural conditions for a countable group acting on a countable tree which imply that the orbit equivalence relation of the induced action on the Gromov boundary is Borel hyperfinite. Examples of this condition include acylindrical actions. We also identify a natural weakening of the aforementioned conditions that implies measure hyperfiniteness of the boundary action. We then document examples of group actions on trees whose boundary action is not hyperfinite.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"36 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744759","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}

{"title":"Strichartz type estimates for solutions to the Schrödinger equation","authors":"Jie Chen","doi":"10.1090/proc/16887","DOIUrl":"https://doi.org/10.1090/proc/16887","url":null,"abstract":"&lt;p&gt;In this article, we show the necessary and sufficient conditions for the inequality &lt;disp-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-vertical-bar u double-vertical-bar Subscript upper L Sub Subscript t Sub Superscript q Subscript upper L Sub Subscript x Sub Superscript r Subscript Baseline less-than-or-equivalent-to double-vertical-bar u double-vertical-bar Subscript upper X Sub Superscript s comma b Subscript Baseline comma\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mo fence=\"false\" stretchy=\"false\"&gt;‖&lt;/mml:mo&gt; &lt;mml:mi&gt;u&lt;/mml:mi&gt; &lt;mml:msub&gt; &lt;mml:mo fence=\"false\" stretchy=\"false\"&gt;‖&lt;/mml:mo&gt; &lt;mml:mrow&gt; &lt;mml:msubsup&gt; &lt;mml:mi&gt;L&lt;/mml:mi&gt; &lt;mml:mi&gt;t&lt;/mml:mi&gt; &lt;mml:mi&gt;q&lt;/mml:mi&gt; &lt;/mml:msubsup&gt; &lt;mml:msubsup&gt; &lt;mml:mi&gt;L&lt;/mml:mi&gt; &lt;mml:mi&gt;x&lt;/mml:mi&gt; &lt;mml:mi&gt;r&lt;/mml:mi&gt; &lt;/mml:msubsup&gt; &lt;/mml:mrow&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;≲&lt;/mml:mo&gt; &lt;mml:mo fence=\"false\" stretchy=\"false\"&gt;‖&lt;/mml:mo&gt; &lt;mml:mi&gt;u&lt;/mml:mi&gt; &lt;mml:msub&gt; &lt;mml:mo fence=\"false\" stretchy=\"false\"&gt;‖&lt;/mml:mo&gt; &lt;mml:mrow&gt; &lt;mml:msup&gt; &lt;mml:mi&gt;X&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;s&lt;/mml:mi&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mi&gt;b&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:msup&gt; &lt;/mml:mrow&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;begin{equation*} |u|_{L_t^qL_x^r}lesssim |u|_{X^{s,b}}, end{equation*}&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/disp-formula&gt; where &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-vertical-bar u double-vertical-bar Subscript upper X Sub Superscript s comma b Baseline colon-equal double-vertical-bar ModifyingAbove u With caret left-parenthesis tau comma xi right-parenthesis mathematical left-angle xi mathematical right-angle Superscript s Baseline mathematical left-angle tau plus StartAbsoluteValue xi EndAbsoluteValue squared mathematical right-angle Superscript b Baseline double-vertical-bar Subscript upper L Sub Subscript tau comma xi Sub Superscript 2\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mo fence=\"false\" stretchy=\"false\"&gt;‖&lt;/mml:mo&gt; &lt;mml:mi&gt;u&lt;/mml:mi&gt; &lt;mml:msub&gt; &lt;mml:mo fence=\"false\" stretchy=\"false\"&gt;‖&lt;/mml:mo&gt; &lt;mml:mrow&gt; &lt;mml:msup&gt; &lt;mml:mi&gt;X&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;s&lt;/mml:mi&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mi&gt;b&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:msup&gt; &lt;/mml:mrow&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;≔&lt;/mml:mo&gt; &lt;mml:mo fence=\"false\" stretchy=\"false\"&gt;‖&lt;/mml:mo&gt; &lt;mml:mrow&gt; &lt;mml:mover&gt; &lt;mml:mi&gt;u&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;^&lt;/mml:mo&gt; &lt;/mml:mover&gt; &lt;/mml:mrow&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;τ&lt;/mml:mi&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mi&gt;ξ&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;mml:mo fence=\"false\" stretchy=\"false\"&gt;⟨&lt;/mml:mo&gt; &lt;mml:mi&gt;ξ&lt;/mml:mi&gt; &lt;mml:msup&gt; &lt;mml:mo fence=\"false\" stretchy=\"false\"&gt;⟩&lt;/mml:mo&gt; &lt;mml:mi&gt;s&lt;/mml:mi&gt; &lt;/mml:msup&gt; &lt;mml:mo fence=\"false\" stretchy=\"false\"&gt;⟨&lt;/mml:mo&gt; &lt;mml:mi&gt;τ&lt;/mml:mi&gt; &lt;mml:mo&gt;+&lt;/mml:mo&gt; &lt;mml:mrow&gt; &lt;mml:mo stretchy=\"false\"&gt;|&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:mi&gt;ξ&lt;/mml:mi&gt; &lt;mml:msup&gt; &lt;mml:mrow&gt; &lt;mml:mo stretchy=\"false\"&gt;|&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;m","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"47 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744657","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}

{"title":"Nikishin’s theorem and factorization through Marcinkiewicz spaces","authors":"Mieczysław Mastyło, Enrique Sánchez Pérez","doi":"10.1090/proc/16888","DOIUrl":"https://doi.org/10.1090/proc/16888","url":null,"abstract":"<p>Consider <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript 0\"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">L^0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F\"> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding=\"application/x-tex\">F</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-space of all equivalence classes of measurable functions on a finite measure space equipped with the topology of convergence in measure. Inspired by Nikishin’s classical result on the factorization of sublinear continuous operators from a Banach space to <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript 0\"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">L^0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we prove a theorem that characterizes those maps from any quasi-metric space into <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript 0\"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">L^0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> that factor strongly through Marcinkiewicz weighted spaces. We show applications to sublinear operators on a certain class of quasi-Banach spaces with generalized Rademacher type generated by Orlicz sequence spaces.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"39 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945161","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}

{"title":"A remark on a paper by F. Chiarenza and M. Frasca","authors":"N. Krylov","doi":"10.1090/proc/16885","DOIUrl":"https://doi.org/10.1090/proc/16885","url":null,"abstract":"<p>In 1990 F. Chiarenza and M. Frasca published a paper in which they generalized a result of C. Fefferman on estimates of the integral of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"StartAbsoluteValue b u EndAbsoluteValue Superscript p\"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mi>b</mml:mi> <mml:mi>u</mml:mi> <mml:msup> <mml:mrow> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">|bu|^{p}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> through the integral of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"StartAbsoluteValue upper D u EndAbsoluteValue Superscript p\"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mi>D</mml:mi> <mml:mi>u</mml:mi> <mml:msup> <mml:mrow> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">|Du|^{p}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p greater-than 1\"> <mml:semantics> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">p&gt;1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Formally their proof is valid only for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d greater-than-or-equal-to 3\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">dgeq 3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We present here further generalization with a different proof in which <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper D\"> <mml:semantics> <mml:mi>D</mml:mi> <mml:annotation encoding=\"application/x-tex\">D</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is replaced with the fractional power of the Laplacian for any dimension <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d greater-than-or-equal-to 2\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">dgeq 2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"2 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142197124","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}

{"title":"On Pólya’s random walk constants","authors":"Robert Gaunt, Saralees Nadarajah, Tibor Pogány","doi":"10.1090/proc/16854","DOIUrl":"https://doi.org/10.1090/proc/16854","url":null,"abstract":"<p>A celebrated result in probability theory is that a simple symmetric random walk on the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d\"> <mml:semantics> <mml:mi>d</mml:mi> <mml:annotation encoding=\"application/x-tex\">d</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimensional lattice <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper Z Superscript d\"> <mml:semantics> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">Z</mml:mi> </mml:mrow> <mml:mi>d</mml:mi> </mml:msup> <mml:annotation encoding=\"application/x-tex\">mathbb {Z}^d</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is recurrent for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d equals 1 comma 2\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">d=1,2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and transient for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d greater-than-or-equal-to 3\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">dgeq 3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In this note, we derive a closed-form expression, in terms of the Lauricella function <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F Subscript upper C\"> <mml:semantics> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>C</mml:mi> </mml:msub> <mml:annotation encoding=\"application/x-tex\">F_C</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, for the return probability for all <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d greater-than-or-equal-to 3\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">dgeq 3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Previously, a closed-form formula had only been available for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d equals 3\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">d=3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"22 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503309","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}

{"title":"Stabilisation of waves on product manifolds by boundary strips","authors":"Ruoyu Wang","doi":"10.1090/proc/16242","DOIUrl":"https://doi.org/10.1090/proc/16242","url":null,"abstract":"<p>We show that a transversely geometrically controlling boundary damping strip is sufficient but not necessary for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"t Superscript negative 1 slash 2\"> <mml:semantics> <mml:msup> <mml:mi>t</mml:mi> <mml:mrow> <mml:mo>−<!-- − --></mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">t^{-1/2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-decay of waves on product manifolds. We give a general scheme to turn resolvent estimates for impedance problems on cross-sections to wave decay on product manifolds.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"39 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938846","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}