Journal of Functional Analysis最新文献_第3页

On the closability of differential operators 关于微分算子的可闭性

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-04-29 DOI: 10.1016/j.jfa.2025.111029

Giovanni Alberti , David Bate , Andrea Marchese

{"title":"On the closability of differential operators","authors":"Giovanni Alberti , David Bate , Andrea Marchese","doi":"10.1016/j.jfa.2025.111029","DOIUrl":"10.1016/j.jfa.2025.111029","url":null,"abstract":"<div><div>We discuss the closability of directional derivative operators with respect to a general Radon measure <em>μ</em> on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>; our main theorem completely characterizes the vectorfields for which the corresponding operator is closable from the space of Lipschitz functions <span><math><mrow><mi>Lip</mi></mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span> to <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></math></span>, for <span><math><mn>1</mn><mo>≤</mo><mi>p</mi><mo>≤</mo><mo>∞</mo></math></span>. We also discuss the closability of the same operators from <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></math></span> to <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></math></span>, and give necessary and sufficient conditions for closability, but we do not have an exact characterization.</div><div>As a corollary we obtain that classical differential operators such as gradient, divergence and Jacobian determinant are closable from <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></math></span> to <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></math></span> only if <em>μ</em> is absolutely continuous with respect to the Lebesgue measure.</div><div>We finally consider the closability of a certain class of multilinear differential operators; these results are then rephrased in terms of metric currents.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 7","pages":"Article 111029"},"PeriodicalIF":1.7,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143923573","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}

引用次数: 0

On the continuity of Følner averages 关于Følner平均的连续性

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-04-29 DOI: 10.1016/j.jfa.2025.111039

Gabriel Fuhrmann , Maik Gröger , Till Hauser

{"title":"On the continuity of Følner averages","authors":"Gabriel Fuhrmann , Maik Gröger , Till Hauser","doi":"10.1016/j.jfa.2025.111039","DOIUrl":"10.1016/j.jfa.2025.111039","url":null,"abstract":"<div><div>It is known that if each point <em>x</em> of a dynamical system is generic for some invariant measure <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span>, then there is a strong connection between certain ergodic and topological properties of that system. In particular, if the acting group is abelian and the map <span><math><mi>x</mi><mo>↦</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span> is continuous, then every orbit closure is uniquely ergodic.</div><div>In this note, we show that if the acting group is not abelian, orbit closures may well support more than one ergodic measure even if <span><math><mi>x</mi><mo>↦</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span> is continuous. We provide examples of such a situation via actions of the group of all orientation-preserving homeomorphisms on the unit interval as well as the Lamplighter group. To discuss these examples, we need to extend the existing theory of weakly mean equicontinuous group actions to allow for multiple ergodic measures on orbit closures and to allow for actions of general amenable groups. These extensions are achieved by adopting an operator-theoretic approach.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 7","pages":"Article 111039"},"PeriodicalIF":1.7,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143942789","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}

引用次数: 0

The free elastic flow for closed planar curves 平面闭合曲线的自由弹性流

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-04-29 DOI: 10.1016/j.jfa.2025.111030

Tatsuya Miura , Glen Wheeler

引用次数: 0

Type II singularities of Lagrangian mean curvature flow with zero Maslov class 零马斯洛夫类拉格朗日平均曲率流的II型奇异性

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-04-29 DOI: 10.1016/j.jfa.2025.111032

Xiang Li , Yong Luo , Jun Sun

引用次数: 0

The Helton-Howe trace formula for the Drury-Arveson space Drury-Arveson空间的Helton-Howe迹公式

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-04-29 DOI: 10.1016/j.jfa.2025.111037

Jingbo Xia

引用次数: 0

The Cauchy problem for the quadratic beam equation in d ≥ 2 d中二次梁方程的柯西问题 ≥ 2

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-04-29 DOI: 10.1016/j.jfa.2025.111041

Zihao Song

引用次数: 0

On the equivalence of distributional and synthetic Ricci curvature lower bounds 分布里奇曲率下界与合成里奇曲率下界的等价性

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-04-29 DOI: 10.1016/j.jfa.2025.111035

Andrea Mondino, Vanessa Ryborz

引用次数: 0

Functional calculus of quantum channels for the holomorphic discrete series of SU(1,1) SU（1,1）全纯离散级数的量子通道泛函演算

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-04-28 DOI: 10.1016/j.jfa.2025.111036

Robin van Haastrecht

{"title":"Functional calculus of quantum channels for the holomorphic discrete series of SU(1,1)","authors":"Robin van Haastrecht","doi":"10.1016/j.jfa.2025.111036","DOIUrl":"10.1016/j.jfa.2025.111036","url":null,"abstract":"<div><div>The tensor product of two holomorphic discrete series representations of <span><math><mi>S</mi><mi>U</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> can be decomposed as a direct multiplicity-free sum of infinitely many holomorphic discrete series representations. I shall introduce equivariant quantum channels for each component of the direct sum by mapping the tensor product of an operator and the identity onto the projection onto one of the irreducible components, generalizing the construction of pure equivariant quantum channels for compact groups. Then I calculate the functional calculus of this operator for polynomials and prove a limit formula for the trace of the functional calculus for any differentiable function. The methods I used are the theory of reproducing kernel Hilbert spaces and a Plancherel theorem for the disk <span><math><mi>D</mi><mo>=</mo><mi>S</mi><mi>U</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo><mo>/</mo><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span>, together with exact constants for the eigenvalues of the Berezin transform. I prove that the limit of the trace of the functional calculus can be expressed using generalized Husimi functions or using Berezin transforms.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 111036"},"PeriodicalIF":1.7,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143907574","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}

引用次数: 0

Schatten classes and commutators of Riesz transforms in the two weight setting Schatten类和Riesz变换的换向子在两种权值设置下

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-04-28 DOI: 10.1016/j.jfa.2025.111028

Michael Lacey , Ji Li , Brett D. Wick , Liangchuan Wu

{"title":"Schatten classes and commutators of Riesz transforms in the two weight setting","authors":"Michael Lacey , Ji Li , Brett D. Wick , Liangchuan Wu","doi":"10.1016/j.jfa.2025.111028","DOIUrl":"10.1016/j.jfa.2025.111028","url":null,"abstract":"<div><div>We characterize the Schatten class <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> of the commutator of Riesz transforms <span><math><mo>[</mo><mi>b</mi><mo>,</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>]</mo></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> (<span><math><mi>j</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>n</mi></math></span>) in the two weight setting for <span><math><mi>n</mi><mo><</mo><mi>p</mi><mo><</mo><mo>∞</mo></math></span>, by introducing the condition that the symbol <em>b</em> is in Besov spaces associated with the given two weights. At the critical index <span><math><mi>p</mi><mo>=</mo><mi>n</mi></math></span>, the commutator <span><math><mo>[</mo><mi>b</mi><mo>,</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>]</mo></math></span> belongs to Schatten class <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> if and only if <em>b</em> is a constant, and to the weak Schatten class <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>,</mo><mo>∞</mo></mrow></msup></math></span> if and only if <em>b</em> is in an oscillation sequence space associated with the given two weights. As a direct application, we have the Schatten class estimate for A. Connes' quantized derivative in the two weight setting.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 111028"},"PeriodicalIF":1.7,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143907575","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}

引用次数: 0

Cartan semigroups and twisted groupoid C*-algebras Cartan半群与扭曲群C*-代数

IF 1.7 2区数学

Journal of Functional Analysis Pub Date : 2025-04-28 DOI: 10.1016/j.jfa.2025.111038

Tristan Bice , Lisa Orloff Clark , Ying-Fen Lin , Kathryn McCormick

引用次数: 0