Transactions of the American Mathematical Society最新文献

{"title":"Bounded Palais-Smale sequences with Morse type information for some constrained functionals","authors":"Jack Borthwick, Xiaojun Chang, Louis Jeanjean, Nicola Soave","doi":"10.1090/tran/9145","DOIUrl":"https://doi.org/10.1090/tran/9145","url":null,"abstract":"<p>In this paper, we study, for functionals having a minimax geometry on a constraint, the existence of bounded Palais-Smale sequences carrying Morse index type information.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal transport and timelike lower Ricci curvature bounds on Finsler spacetimes","authors":"Mathias Braun, Shin-ichi Ohta","doi":"10.1090/tran/9126","DOIUrl":"https://doi.org/10.1090/tran/9126","url":null,"abstract":"<p>We prove that a Finsler spacetime endowed with a smooth reference measure whose induced weighted Ricci curvature <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper R normal i normal c Subscript upper N\"> <mml:semantics> <mml:msub> <mml:mrow> <mml:mi mathvariant=\"normal\">R</mml:mi> <mml:mi mathvariant=\"normal\">i</mml:mi> <mml:mi mathvariant=\"normal\">c</mml:mi> </mml:mrow> <mml:mi>N</mml:mi> </mml:msub> <mml:annotation encoding=\"application/x-tex\">mathrm {Ric}_N</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is bounded from below by a real number <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> in every timelike direction satisfies the timelike curvature-dimension condition <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper T normal upper C normal upper D Subscript q Baseline left-parenthesis upper K comma upper N right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant=\"normal\">T</mml:mi> <mml:mi mathvariant=\"normal\">C</mml:mi> <mml:mi mathvariant=\"normal\">D</mml:mi> </mml:mrow> <mml:mi>q</mml:mi> </mml:msub> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>K</mml:mi> <mml:mo>,</mml:mo> <mml:mi>N</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathrm {TCD}_q(K,N)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for all <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q element-of left-parenthesis 0 comma 1 right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">qin (0,1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The converse and a nonpositive-dimensional version (<inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N less-than-or-equal-to 0\"> <mml:semantics> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">N le 0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>) of this result are also shown. Our discussion is based on the solvability of the Monge problem with respect to the <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> </i","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140935053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The solid-fluid transmission problem","authors":"Nikolas Eptaminitakis, Plamen Stefanov","doi":"10.1090/tran/9016","DOIUrl":"https://doi.org/10.1090/tran/9016","url":null,"abstract":"<p>We study microlocally the transmission problem at the interface between an isotropic linear elastic solid and a linear inviscid fluid. We set up a system of evolution equations describing the particle displacement and velocity in the solid, and pressure and velocity in the fluid, coupled by suitable transmission conditions at the interface. We show well-posedness for the coupled system and study the problem microlocally, constructing a parametrix for it using geometric optics. This construction describes the reflected and transmitted waves, including mode converted ones, related to incoming waves from either side. We also study formation of surface Scholte waves. Finally, we prove that under suitable assumptions, we can recover the s- and the p-speeds, as well as the speed of the liquid, from boundary measurements.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New tensor products of C*-algebras and characterization of type I C*-algebras as rigidly symmetric C*-algebras","authors":"Hun Hee Lee, Ebrahim Samei, Matthew Wiersma","doi":"10.1090/tran/9139","DOIUrl":"https://doi.org/10.1090/tran/9139","url":null,"abstract":"<p>Inspired by recent developments in the theory of Banach and operator algebras of locally compact groups, we construct several new classes of bifunctors <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis upper A comma upper B right-parenthesis right-arrow from bar upper A circled-times Subscript alpha Baseline upper B\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>A</mml:mi> <mml:mo>,</mml:mo> <mml:mi>B</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo stretchy=\"false\">↦<!-- ↦ --></mml:mo> <mml:mi>A</mml:mi> <mml:msub> <mml:mo>⊗<!-- ⊗ --></mml:mo> <mml:mrow> <mml:mi>α<!-- α --></mml:mi> </mml:mrow> </mml:msub> <mml:mi>B</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">(A,B)mapsto Aotimes _{alpha } B</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A circled-times Subscript alpha Baseline upper B\"> <mml:semantics> <mml:mrow> <mml:mi>A</mml:mi> <mml:msub> <mml:mo>⊗<!-- ⊗ --></mml:mo> <mml:mi>α<!-- α --></mml:mi> </mml:msub> <mml:mi>B</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">Aotimes _alpha B</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a cross norm completion of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A circled-dot upper B\"> <mml:semantics> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>⊙<!-- ⊙ --></mml:mo> <mml:mi>B</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">Aodot B</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for each pair of C*-algebras <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A\"> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=\"application/x-tex\">A</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=\"upper B\"> <mml:semantics> <mml:mi>B</mml:mi> <mml:annotation encoding=\"application/x-tex\">B</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. For the first class of bifunctors considered <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis upper A comma upper B right-parenthesis right-arrow from bar upper A circled-times Subscript p Baseline upper B\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>A</mml:mi> <mml:mo>,</mml:mo> <mml:mi>B</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo stretchy=\"false\">↦<!-- ↦ --></mml:mo> <mml:mi>A</mml:mi> <mml:mrow> <mml:msub> <mml:mo>⊗<!-- ⊗ --></mml:mo> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">(A,B)maps","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140935131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Gelfand–Phillips and Dunford–Pettis type properties in bimodules of measurable operators","authors":"Jinghao Huang, Yerlan Nessipbayev, Marat Pliev, Fedor Sukochev","doi":"10.1090/tran/9117","DOIUrl":"https://doi.org/10.1090/tran/9117","url":null,"abstract":"<p>We fully characterize noncommutative symmetric spaces <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E left-parenthesis script upper M comma tau right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mrow> <mml:mi mathvariant=\"script\">M</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mi>τ</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">E(mathcal {M},tau )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> affiliated with a semifinite von Neumann algebra <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper M\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"script\">M</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathcal {M}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> equipped with a faithful normal semifinite trace <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"tau\"> <mml:semantics> <mml:mi>τ</mml:mi> <mml:annotation encoding=\"application/x-tex\">tau</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on a (not necessarily separable) Hilbert space having the Gelfand–Phillips property and the WCG-property. The complete list of their relations with other classical structural properties (such as the Dunford–Pettis property, the Schur property and their variations) is given in the general setting of noncommutative symmetric spaces.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Moments and asymptotics for a class of SPDEs with space-time white noise","authors":"Le Chen, Yuhui Guo, Jian Song","doi":"10.1090/tran/9138","DOIUrl":"https://doi.org/10.1090/tran/9138","url":null,"abstract":"<p>In this article, we consider the nonlinear stochastic partial differential equation of fractional order in both space and time variables with constant initial condition: <disp-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis partial-differential Subscript t Superscript beta Baseline plus StartFraction nu Over 2 EndFraction left-parenthesis negative normal upper Delta right-parenthesis Superscript alpha slash 2 Baseline right-parenthesis u left-parenthesis t comma x right-parenthesis equals upper I Subscript t Superscript gamma Baseline left-bracket lamda u left-parenthesis t comma x right-parenthesis ModifyingAbove upper W With dot left-parenthesis t comma x right-parenthesis right-bracket t greater-than 0 comma x element-of double-struck upper R Superscript d Baseline comma\"> <mml:semantics> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:msubsup> <mml:mi mathvariant=\"normal\">∂<!-- ∂ --></mml:mi> <mml:mi>t</mml:mi> <mml:mrow> <mml:mi>β<!-- β --></mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>+</mml:mo> <mml:mstyle displaystyle=\"true\" scriptlevel=\"0\"> <mml:mfrac> <mml:mi>ν<!-- ν --></mml:mi> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mstyle> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>−<!-- − --></mml:mo> <mml:mi mathvariant=\"normal\">Δ<!-- Δ --></mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>α<!-- α --></mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>u</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>,</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:mspace width=\"mediummathspace\" /> <mml:msubsup> <mml:mi>I</mml:mi> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>γ<!-- γ --></mml:mi> </mml:mrow> </mml:msubsup> <mml:mrow> <mml:mo>[</mml:mo> <mml:mi>λ<!-- λ --></mml:mi> <mml:mi>u</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>,</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mrow> <mml:mover> <mml:mi>W</mml:mi> <mml:mo>˙<!-- ˙ --></mml:mo> </mml:mover> </mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>,</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>]</mml:mo> </mml:mrow> <mml:mspace width=\"1em\" /> <mml:mi>t</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mspace width=\"mediummathspace\" /> <mml:mi>x</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mi>d</mml:mi> </mml:msup> <mml:mo>,</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">begin{equation*} left (partial ^{beta }_t+dfrac {nu }{2}left (-Delta right )^{alpha / 2}right ) u(t, x) = : I_{t}^{gamma }left [lambda u(t, x) dot {W}(t, x)right ] quad t&gt;0,: xin mathbb {R}^d, end{equation*}</mml:annotation> </mml:semantics> </mml:math> </disp-formula> with ","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Steinberg quotients, Weyl characters, and Kazhdan-Lusztig polynomials","authors":"Paul Sobaje","doi":"10.1090/tran/9132","DOIUrl":"https://doi.org/10.1090/tran/9132","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a reductive group over a field of prime characteristic. An indecomposable tilting module for <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> whose highest weight lies above the Steinberg weight has a character that is divisible by the Steinberg character. The resulting “Steinberg quotient” carries important information about <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-modules, and in previous work we studied patterns in the weight multiplicities of these characters. In this paper we broaden our scope to include quantum Steinberg quotients, and show how the multiplicities in these characters relate to algebraic Steinberg quotients, Weyl characters, and evaluations of Kazhdan-Lusztig polynomials. We give an explicit algorithm for computing minimal characters that possess a key attribute of Steinberg quotients. We provide computations which show that these minimal characters are not always equal to quantum Steinberg quotients, but are close in several nontrivial cases.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hausdorff dimension of the Cartesian product of limsup sets in Diophantine approximation","authors":"Baowei Wang, Jun Wu","doi":"10.1090/tran/9136","DOIUrl":"https://doi.org/10.1090/tran/9136","url":null,"abstract":"<p>The metric theory of limsup sets is the main topic in metric Diophantine approximation. A very simple observation by Erdös shows the dimension of the Cartesian product of two sets of Liouville numbers is 1. To disclose the mystery hidden there, we consider and present a general principle for the Hausdorff dimension of the Cartesian product of limsup sets. As an application of our general principle, it is found that <disp-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"dimension Subscript script upper H Baseline upper W left-parenthesis psi right-parenthesis times midline-horizontal-ellipsis times upper W left-parenthesis psi right-parenthesis equals d minus 1 plus dimension Subscript script upper H Baseline upper W left-parenthesis psi right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>dim</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant=\"script\">H</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> <mml:mo>⁡<!-- ⁡ --></mml:mo> <mml:mi>W</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>ψ<!-- ψ --></mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>×<!-- × --></mml:mo> <mml:mo>⋯<!-- ⋯ --></mml:mo> <mml:mo>×<!-- × --></mml:mo> <mml:mi>W</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>ψ<!-- ψ --></mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>d</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:msub> <mml:mi>dim</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant=\"script\">H</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> <mml:mo>⁡<!-- ⁡ --></mml:mo> <mml:mi>W</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>ψ<!-- ψ --></mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">begin{equation*} dim _{mathcal H}W(psi )times cdots times W(psi )=d-1+dim _{mathcal H}W(psi ) end{equation*}</mml:annotation> </mml:semantics> </mml:math> </disp-formula> where <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper W left-parenthesis psi right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>W</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>ψ<!-- ψ --></mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">W(psi )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the set of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"psi\"> <mml:semantics> <mml:mi>ψ<!-- ψ --></mml:mi> <mml:annotation encoding=\"application/x-tex\">psi</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-well approximable points in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper R\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathbb {R}</mml:annotation> </","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Simply interpolating sequences in complete Pick spaces","authors":"Nikolaos Chalmoukis, Alberto Dayan, Michael Hartz","doi":"10.1090/tran/9123","DOIUrl":"https://doi.org/10.1090/tran/9123","url":null,"abstract":"<p>We characterize simply interpolating sequences (also known as onto interpolating sequences) for complete Pick spaces. We show that a sequence is simply interpolating if and only if it is strongly separated. This answers a question of Agler and M^cCarthy. Moreover, we show that in many important examples of complete Pick spaces, including weighted Dirichlet spaces on the unit disc and the Drury–Arveson space in finitely many variables, simple interpolation does not imply multiplier interpolation. In fact, in those spaces, we construct simply interpolating sequences that generate infinite measures, and uniformly separated sequences that are not multiplier interpolating.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Boundedness and compactness of Hausdorff operators on Fock spaces","authors":"Óscar Blasco, Antonio Galbis","doi":"10.1090/tran/9133","DOIUrl":"https://doi.org/10.1090/tran/9133","url":null,"abstract":"<p>We obtain a complete characterization of the bounded Hausdorff operators acting on a Fock space <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F Subscript alpha Superscript p\"> <mml:semantics> <mml:msubsup> <mml:mi>F</mml:mi> <mml:mi>α</mml:mi> <mml:mi>p</mml:mi> </mml:msubsup> <mml:annotation encoding=\"application/x-tex\">F^p_alpha</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and taking its values into a larger one <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F Subscript alpha Superscript q Baseline comma 0 greater-than p less-than-or-equal-to q less-than-or-equal-to normal infinity\"> <mml:semantics> <mml:mrow> <mml:msubsup> <mml:mi>F</mml:mi> <mml:mi>α</mml:mi> <mml:mi>q</mml:mi> </mml:msubsup> <mml:mo>,</mml:mo> <mml:mtext> </mml:mtext> <mml:mn>0</mml:mn> <mml:mo>&gt;</mml:mo> <mml:mi>p</mml:mi> <mml:mo>≤</mml:mo> <mml:mi>q</mml:mi> <mml:mo>≤</mml:mo> <mml:mi mathvariant=\"normal\">∞</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">F^q_alpha , 0 &gt; p leq q leq infty</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, as well as some necessary or sufficient conditions for a Hausdorff operator to transform a Fock space into a smaller one. Some results are written in the context of mixed norm Fock spaces. Also the compactness of Hausdorff operators on a Fock space is characterized. The compactness result for Hausdorff operators on the Fock space <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F Subscript alpha Superscript normal infinity\"> <mml:semantics> <mml:msubsup> <mml:mi>F</mml:mi> <mml:mi>α</mml:mi> <mml:mi mathvariant=\"normal\">∞</mml:mi> </mml:msubsup> <mml:annotation encoding=\"application/x-tex\">F^infty _alpha</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is extended to more general Banach spaces of entire functions with weighted sup norms defined in terms of a radial weight and conditions for the Hausdorff operators to become <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>-summing are also included.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}