Proceedings of the American Mathematical Society最新文献

{"title":"Zeros of a growing number of derivatives of random polynomials with independent roots","authors":"Marcus Michelen, Xuan-Truong Vu","doi":"10.1090/proc/16794","DOIUrl":"https://doi.org/10.1090/proc/16794","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X 1 comma upper X 2 comma ellipsis\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>X</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mo>…</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">X_1,X_2,ldots</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be independent and identically distributed random variables in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper C\"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mi mathvariant=\"double-struck\">C</mml:mi> </mml:mrow> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">{mathbb {C}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> chosen from a probability measure <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"mu\"> <mml:semantics> <mml:mi>μ</mml:mi> <mml:annotation encoding=\"application/x-tex\">mu</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and define the random polynomial <disp-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"StartLayout 1st Row upper P Subscript n Baseline left-parenthesis z right-parenthesis equals left-parenthesis z minus upper X 1 right-parenthesis ellipsis left-parenthesis z minus upper X Subscript n Baseline right-parenthesis period EndLayout\"> <mml:semantics> <mml:mtable columnalign=\"right left right left right left right left right left right left\" rowspacing=\"3pt\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\" side=\"left\" displaystyle=\"true\"> <mml:mtr> <mml:mtd> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>…</mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mspace width=\"thinmathspace\"/> <mml:mo>.</mml:mo> </mml:mtd> </mml:mtr> </mml:mtable> <mml:annotation encoding=\"application/x-tex\">begin{align*} P_n(z)=(z-X_1)ldots (z-X_n),. end{align*}</mml:annotation> </mml:semantics> </mml:math> </disp-formula> We show that for any sequence <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k equals k left-parenthesis n right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>=</mml:mo> <mml:mi>k</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"44 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938753","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 representation of sup-completion","authors":"Achintya Polavarapu, Vladimir Troitsky","doi":"10.1090/proc/16796","DOIUrl":"https://doi.org/10.1090/proc/16796","url":null,"abstract":"<p>It was showed by Donner in [<italic>Extension of positive operators and Korovkin theorems</italic>, Lecture Notes in Mathematics, vol. 904, Springer-Verlag, Berlin-New York, 1982] that every order complete vector lattice <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\"application/x-tex\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> may be embedded into a cone <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X Superscript s\"> <mml:semantics> <mml:msup> <mml:mi>X</mml:mi> <mml:mi>s</mml:mi> </mml:msup> <mml:annotation encoding=\"application/x-tex\">X^s</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, called the sup-completion of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper 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 if one represents the universal completion of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\"application/x-tex\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> as <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript normal infinity Baseline left-parenthesis upper K right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>C</mml:mi> <mml:mi mathvariant=\"normal\">∞</mml:mi> </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\">C^infty (K)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, then <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X Superscript s\"> <mml:semantics> <mml:msup> <mml:mi>X</mml:mi> <mml:mi>s</mml:mi> </mml:msup> <mml:annotation encoding=\"application/x-tex\">X^s</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the set of all continuous functions from <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> to <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-bracket negative normal infinity comma normal infinity right-bracket\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\">[</mml:mo> <mml:mo>−</mml:mo> <mml:mi mathvariant=\"normal\">∞</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant=\"normal\">∞","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"11 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141516776","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":"Products of hyperelliptic Jacobians with maximal Galois image","authors":"Jędrzej Garnek","doi":"10.1090/proc/16628","DOIUrl":"https://doi.org/10.1090/proc/16628","url":null,"abstract":"<p>In this note we study the associated adelic representation of a product of hyperelliptic Jacobians. We give a simple criterion that ensures that this representation has maximal Galois image in a certain sense. As an application, we provide a method of constructing products of Jacobians with division fields as disjoint as they can be.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"44 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938857","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":"Indecomposability of the bounded derived categories of Brill-Noether varieties","authors":"Xun Lin, Chenglong Yu","doi":"10.1090/proc/16654","DOIUrl":"https://doi.org/10.1090/proc/16654","url":null,"abstract":"<p>We prove that the bounded derived category of coherent sheaves of the Brill-Noether variety <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G Subscript d Superscript r Baseline left-parenthesis upper C right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msubsup> <mml:mi>G</mml:mi> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>C</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">G^{r}_{d}(C)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> parametrizing linear series of degree <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> and dimension <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"r\"> <mml:semantics> <mml:mi>r</mml:mi> <mml:annotation encoding=\"application/x-tex\">r</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on a general smooth projective curve <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C\"> <mml:semantics> <mml:mi>C</mml:mi> <mml:annotation encoding=\"application/x-tex\">C</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is indecomposable when <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d less-than-or-equal-to g left-parenthesis upper C right-parenthesis minus 1\"> <mml:semantics> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mi>g</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>C</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>−<!-- − --></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">dleq g(C)-1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"32 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938847","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":"The stable conjugation-invariant word norm is rational in free groups","authors":"Henry Jaspars","doi":"10.1090/proc/16786","DOIUrl":"https://doi.org/10.1090/proc/16786","url":null,"abstract":"<p>We establish the rationality of the stable conjugation-invariant word norm on free groups and virtually free Coxeter groups.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"81 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938822","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":"Classifying solutions of 𝑆𝑈(𝑛+1) Toda system around a singular source","authors":"Jingyu Mu, Yiqian Shi, Tianyang Sun, Bin Xu","doi":"10.1090/proc/16785","DOIUrl":"https://doi.org/10.1090/proc/16785","url":null,"abstract":"&lt;p&gt;Consider a positive integer &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;n&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; and &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"gamma 1 greater-than negative 1 comma midline-horizontal-ellipsis comma gamma Subscript n Baseline greater-than negative 1\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;γ&lt;!-- γ --&gt;&lt;/mml:mi&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;&gt;&lt;/mml:mo&gt; &lt;mml:mo&gt;−&lt;!-- − --&gt;&lt;/mml:mo&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mo&gt;⋯&lt;!-- ⋯ --&gt;&lt;/mml:mo&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;γ&lt;!-- γ --&gt;&lt;/mml:mi&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;&gt;&lt;/mml:mo&gt; &lt;mml:mo&gt;−&lt;!-- − --&gt;&lt;/mml:mo&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;gamma _1&gt;-1,cdots ,gamma _n&gt;-1&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;. Let &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper D equals StartSet z element-of double-struck upper C colon StartAbsoluteValue z EndAbsoluteValue greater-than 1 EndSet\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;D&lt;/mml:mi&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;z&lt;/mml:mi&gt; &lt;mml:mo&gt;∈&lt;!-- ∈ --&gt;&lt;/mml:mo&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"double-struck\"&gt;C&lt;/mml:mi&gt; &lt;/mml:mrow&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;z&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mo stretchy=\"false\"&gt;|&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:mo&gt;&gt;&lt;/mml:mo&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;mml:mo fence=\"false\" stretchy=\"false\"&gt;}&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;D={zin mathbb {C}:|z|&gt;1}&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;, and let &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis a Subscript i j Baseline right-parenthesis Subscript n times n\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;a&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;i&lt;/mml:mi&gt; &lt;mml:mi&gt;j&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:msub&gt; &lt;mml:msub&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;mml:mo&gt;×&lt;!-- × --&gt;&lt;/mml:mo&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:msub&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;(a_{ij})_{ntimes n}&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; denote the Cartan matrix of &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"German s German u German left-parenthesis German n German plus German 1 German right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"fraktur\"&gt;s&lt;/mml:mi&gt; &lt;mml:mi mathvariant=\"fraktur\"&gt;u&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mo mathvariant=\"fraktur\" stretchy=","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"44 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938834","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":"Double-well phase transitions are more rigid than minimal hypersurfaces","authors":"Christos Mantoulidis","doi":"10.1090/proc/16636","DOIUrl":"https://doi.org/10.1090/proc/16636","url":null,"abstract":"<p>In this short note we see that double-well phase transitions exhibit more rigidity than their minimal hypersurface counterparts.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"23 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938844","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":"Linear asymptotic stability of small-amplitude periodic waves of the generalized Korteweg–de Vries equations","authors":"Corentin Audiard, L. Rodrigues, Changzhen Sun","doi":"10.1090/proc/16778","DOIUrl":"https://doi.org/10.1090/proc/16778","url":null,"abstract":"<p>We extend the detailed study of the linearized dynamics obtained for cnoidal waves of the Korteweg–de Vries equation by Rodrigues [J. Funct. Anal. 274 (2018), pp. 2553–2605] to small-amplitude periodic traveling waves of the generalized Korteweg–de Vries equations that are not subject to Benjamin–Feir instability. With the adapted notion of stability, this provides for such waves, global-in-time bounded stability in any Sobolev space, and asymptotic stability of dispersive type. When doing so, we actually prove that such results also hold for waves of arbitrary amplitude satisfying a form of spectral stability designated here as dispersive spectral stability.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"47 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059939","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 𝐶^{1,𝛼}-smooth approximation of Lipschitz functions","authors":"Michal Johanis","doi":"10.1090/proc/16789","DOIUrl":"https://doi.org/10.1090/proc/16789","url":null,"abstract":"<p>We show that on super-reflexive spaces a Moreau-Yosida type of regularisation by infimal convolution together with a known insertion-type theorem (a variant of Ilmanen’s lemma) easily give an approximation of a Lipschitz function by a <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript 1 comma alpha\"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mi>α</mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding=\"application/x-tex\">C^{1,alpha }</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-smooth Lipschitz function with the same Lipschitz constant. This is a generalisation of the well-known theorem of J.-M. Lasry and P.-L. Lions from Hilbert spaces. It also gives a new self-contained and probably simpler proof of the Lasry-Lions theorem.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"35 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938828","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":"Identification of maximal C*-covers of some operator algebras","authors":"Benton Duncan","doi":"10.1090/proc/16783","DOIUrl":"https://doi.org/10.1090/proc/16783","url":null,"abstract":"<p>We use results on inclusions of free products and extensions of completely positive maps to determine the maximal C<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:mo>∗</mml:mo> </mml:msup> <mml:annotation encoding=\"application/x-tex\">^*</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-envelope for upper triangular <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3 times 3\"> <mml:semantics> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>×</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">3 times 3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> matrices. We consider these same results in the context of larger upper triangular matrices and graph algebras associated to cycle graphs.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"138 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938755","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}