Journal of Functional Analysis最新文献

{"title":"Critical prescribed Q-curvature flow on closed even-dimensional manifolds with sign-changing functions","authors":"Leilei Cui ,&nbsp;Changfeng Gui ,&nbsp;Haicheng Yan ,&nbsp;Wen Yang","doi":"10.1016/j.jfa.2025.111133","DOIUrl":"10.1016/j.jfa.2025.111133","url":null,"abstract":"<div><div>In this article, we consider the prescribed <em>Q</em>-curvature equation<span><span><span><math><mi>P</mi><mi>u</mi><mo>=</mo><mi>ρ</mi><mrow><mo>(</mo><mfrac><mrow><mi>h</mi><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn><mi>n</mi><mi>u</mi></mrow></msup></mrow><mrow><msub><mrow><mo>∫</mo></mrow><mrow><mi>M</mi></mrow></msub><mi>h</mi><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn><mi>n</mi><mi>u</mi></mrow></msup><mi>d</mi><mi>μ</mi></mrow></mfrac><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mo>|</mo><mi>M</mi><msub><mrow><mo>|</mo></mrow><mrow><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msub></mrow></mfrac><mo>)</mo></mrow><mspace></mspace><mspace></mspace><mtext>in</mtext><mspace></mspace><mspace></mspace><mi>M</mi><mo>,</mo></math></span></span></span> where <span><math><mo>(</mo><mi>M</mi><mo>,</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></math></span> is a closed 2<em>n</em>-dimensional Riemannian manifold, <span><math><mi>P</mi></math></span> represents the GJMS operator, which is (weakly) positive with a kernel of constant functions. The function <em>h</em> is smooth and sign-changing, while <em>ρ</em> is a positive constant. In the critical case with <span><math><mi>ρ</mi><mo>=</mo><msup><mrow><mn>4</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>!</mo><msup><mrow><mi>π</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, we employ a negative gradient-like flow method to establish the existence of solutions to this prescribed <em>Q</em>-curvature equation. Our approach extends the work of Li-Xu <span><span>[46]</span></span>, which focused on dimension 2, to general even dimensions. This result can also be viewed as a counterpart to <span><span>[8]</span></span> in the case where <em>h</em> is a sign-changing function.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111133"},"PeriodicalIF":1.7,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144670289","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":"Topological structure of the space of composition operators on the Hardy space of Dirichlet series","authors":"Frédéric Bayart ,&nbsp;Maofa Wang ,&nbsp;Xingxing Yao","doi":"10.1016/j.jfa.2025.111134","DOIUrl":"10.1016/j.jfa.2025.111134","url":null,"abstract":"<div><div>The aim of this paper is to study when two composition operators on the Hilbert space of Dirichlet series with square summable coefficients belong to the same component or when their difference is compact. As a corollary we show that if a linear combination of composition operators with polynomial symbols of degree at most 2 is compact, then each composition operator is compact.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111134"},"PeriodicalIF":1.7,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144656711","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":"On log-concave-tailed chaoses and the restricted isometry property","authors":"Guozheng Dai ,&nbsp;Zhonggen Su ,&nbsp;Vladimir Ulyanov ,&nbsp;Hanchao Wang","doi":"10.1016/j.jfa.2025.111130","DOIUrl":"10.1016/j.jfa.2025.111130","url":null,"abstract":"<div><div>In this paper, we obtain a <em>p</em>-th moment bound for the suprema of a log-concave-tailed nonhomogeneous chaos process, which is optimal in some cases. With this <em>p</em>-th moment bound, we get two uniform Hanson-Wright type deviation inequalities for <em>α</em>-subexponential entries (<span><math><mn>1</mn><mo>≤</mo><mi>α</mi><mo>≤</mo><mn>2</mn></math></span>), which generalize some known results. As applications, we prove the restricted isometry property of partial random circulant matrices and time-frequency structured random matrices induced by <em>α</em>-subexponential vectors (<span><math><mn>1</mn><mo>≤</mo><mi>α</mi><mo>≤</mo><mn>2</mn></math></span>), which extends the previously known results proved in the subgaussian case.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111130"},"PeriodicalIF":1.7,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144656710","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":"Geometric influences on quantum Boolean cubes","authors":"David P. Blecher ,&nbsp;Li Gao ,&nbsp;Bang Xu","doi":"10.1016/j.jfa.2025.111132","DOIUrl":"10.1016/j.jfa.2025.111132","url":null,"abstract":"<div><div>In this work, we study three problems related to the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-influence on quantum Boolean cubes. In the first place, we obtain a dimension free bound for <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-influence, which implies the quantum <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-KKL Theorem result obtained by Rouzé, Wirth and Zhang. Beyond that, we also obtain a high order quantum Talagrand inequality and quantum <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-KKL theorem. Lastly, we prove a quantitative relation between the noise stability and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-influence. To this end, our technique involves the random restrictions method as well as semigroup theory.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111132"},"PeriodicalIF":1.7,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144656709","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":"Computation of weighted Bergman inner products on bounded symmetric domains and restriction to subgroups II","authors":"Ryosuke Nakahama","doi":"10.1016/j.jfa.2025.111131","DOIUrl":"10.1016/j.jfa.2025.111131","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Let &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; be a symmetric pair of holomorphic type, and we consider a pair of Hermitian symmetric spaces &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;⊂&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, realized as bounded symmetric domains in complex vector spaces &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;⊂&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; respectively. Then the universal covering group &lt;span&gt;&lt;math&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;˜&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/math&gt;&lt;/span&gt; of &lt;em&gt;G&lt;/em&gt; acts unitarily on the weighted Bergman space &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;⊂&lt;/mo&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; on &lt;em&gt;D&lt;/em&gt;. Its restriction to the subgroup &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;˜&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; decomposes discretely and multiplicity-freely, and its branching law is given explicitly by Hua–Kostant–Schmid–Kobayashi's formula in terms of the &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;-decomposition of the space &lt;span&gt;&lt;math&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; of polynomials on the orthogonal complement &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; of &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; in &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;. The object of this article is to construct explicitly &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;˜&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;-intertwining operators (symmetry breaking operators) &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;˜&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; from holomorph","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 11","pages":"Article 111131"},"PeriodicalIF":1.7,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144685907","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":"Non-rigidity of the absolutely continuous part of A-free measures","authors":"Luigi De Masi ,&nbsp;Carlo Gasparetto","doi":"10.1016/j.jfa.2025.111114","DOIUrl":"10.1016/j.jfa.2025.111114","url":null,"abstract":"<div><div>We generalize a result by Alberti, showing that, if a first-order linear differential operator <span><math><mi>A</mi></math></span> belongs to a certain class, then any <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> function is the absolutely continuous part of a measure <em>μ</em> satisfying <span><math><mi>A</mi><mi>μ</mi><mo>=</mo><mn>0</mn></math></span>. When <span><math><mi>A</mi></math></span> is scalar valued, we provide a necessary and sufficient condition for the above property to hold true and we prove dimensional estimates on the singular part of <em>μ</em>. Finally, we show that operators in the above class satisfy a Lusin-type property.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 10","pages":"Article 111114"},"PeriodicalIF":1.7,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144572031","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":"Envelopes in the class of Banach algebras of polynomial growth and C∞-functions of a finite number of free variables","authors":"O.Yu. Aristov","doi":"10.1016/j.jfa.2025.111117","DOIUrl":"10.1016/j.jfa.2025.111117","url":null,"abstract":"<div><div>We introduce the notion of envelope of a topological algebra (in particular, an arbitrary associative algebra) with respect to a class of Banach algebras. In the case of the class of real Banach algebras of polynomial growth, i.e., admitting a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-functional calculus for every element, we get a functor that maps the algebra of polynomials in <em>k</em> variables to the algebra of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-functions on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>k</mi></mrow></msup></math></span>. The envelope of a general commutative or non-commutative algebra can be treated as an algebra of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-functions on some commutative or non-commutative space. In particular, we describe the envelopes of the universal enveloping algebra of finite-dimensional Lie algebras, the coordinate algebras of the quantum plane and quantum group <span><math><mi>S</mi><mi>L</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></span> and also look at some commutative examples. A result on algebras of ‘free <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-functions’, i.e., the envelopes of free associative algebras of finite rank <em>k</em>, is announced for general <em>k</em> and proved for <span><math><mi>k</mi><mo>⩽</mo><mn>2</mn></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 10","pages":"Article 111117"},"PeriodicalIF":1.7,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144570100","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":"Spectra of Cantor measures with consecutive digit sets revisited","authors":"Yan-Song Fu ,&nbsp;Chuntai Liu","doi":"10.1016/j.jfa.2025.111111","DOIUrl":"10.1016/j.jfa.2025.111111","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>b</mi><mo>,</mo><mi>q</mi></mrow></msub></math></span> be the self-similar measure satisfying <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>b</mi><mo>,</mo><mi>q</mi></mrow></msub><mo>(</mo><mo>⋅</mo><mo>)</mo><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>q</mi></mrow></mfrac><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>j</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>q</mi><mo>−</mo><mn>1</mn></mrow></msubsup><msub><mrow><mi>μ</mi></mrow><mrow><mi>b</mi><mo>,</mo><mi>q</mi></mrow></msub><mo>(</mo><msubsup><mrow><mi>φ</mi></mrow><mrow><mi>j</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><mo>(</mo><mo>⋅</mo><mo>)</mo><mo>)</mo></math></span>, where <span><math><msub><mrow><mi>φ</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>x</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>j</mi></mrow><mrow><mi>q</mi></mrow></mfrac></math></span>, <span><math><mn>0</mn><mo>≤</mo><mi>j</mi><mo>&lt;</mo><mi>q</mi></math></span> and <span><math><mn>2</mn><mo>≤</mo><mi>q</mi><mo>&lt;</mo><mi>b</mi><mo>∈</mo><mi>Z</mi></math></span> such that <span><math><mi>q</mi><mo>|</mo><mi>b</mi></math></span>. This paper will analyze the orthonormal bases of exponential functions for <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>b</mi><mo>,</mo><mi>q</mi></mrow></msub><mo>)</mo></math></span>. We present a sufficient and necessary condition for discrete sets to be maximal orthogonal sets and a sufficient condition for maximal orthogonal sets to be bases in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>b</mi><mo>,</mo><mi>q</mi></mrow></msub><mo>)</mo></math></span> which generalizes the main results of Dutkay, Han and Sun (2009) for <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mn>4</mn><mo>,</mo><mn>2</mn></mrow></msub></math></span>. Finally, a complete characterization on the structure of spectra for <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>b</mi><mo>,</mo><mi>q</mi></mrow></msub></math></span> is given in the viewpoint of measure and dimension which generalizes one of the main results of Deng, Fu and Kang (2024).</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 10","pages":"Article 111111"},"PeriodicalIF":1.7,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144579255","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":"Strong almost finiteness","authors":"Gábor Elek ,&nbsp;Ádám Timár","doi":"10.1016/j.jfa.2025.111116","DOIUrl":"10.1016/j.jfa.2025.111116","url":null,"abstract":"<div><div>A countable, bounded degree graph is almost finite if it has a tiling with isomorphic copies of finitely many Følner sets, and we call it strongly almost finite, if the tiling can be randomized so that the probability that a vertex is on the boundary of a tile is uniformly small. We give various equivalents for strong almost finiteness. In particular, we prove that Property A together with the Følner property is equivalent to strong almost finiteness. Using these characterizations, we show that graphs of subexponential growth and Schreier graphs of amenable groups are always strongly almost finite, generalizing the celebrated result of Downarowicz, Huczek and Zhang about amenable Cayley graphs, based on graph theoretic rather than group theoretic principles. We give various equivalents to Property A for graphs, and show that if a sequence of graphs of Property A (in a uniform sense) converges to a graph <em>G</em> in the neighborhood distance (a purely combinatorial analogue of the classical Benjamini-Schramm distance), then their Laplacian spectra converge to the Laplacian spectrum of <em>G</em> in the Hausdorff distance. We apply the previous theory to construct a new and rich class of classifiable <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⋆</mo></mrow></msup></math></span>-algebras. Namely, we show that for any minimal strong almost finite graph <em>G</em> there are naturally associated simple, nuclear, stably finite <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⋆</mo></mrow></msup></math></span>-algebras that are classifiable by their Elliott invariants.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 10","pages":"Article 111116"},"PeriodicalIF":1.7,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144572033","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":"Tingley's problem for Schreier spaces and their p - convexifications","authors":"Micheline Fakhoury","doi":"10.1016/j.jfa.2025.111122","DOIUrl":"10.1016/j.jfa.2025.111122","url":null,"abstract":"<div><div>We describe the surjective isometries of the unit sphere of real Schreier spaces of all orders and their <em>p</em> <!-->-<!--> <!-->convexifications, for <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mo>∞</mo></math></span>. This description allows us to provide for those spaces a positive answer to a special case of Tingley's problem, which asks whether every surjective isometry of the unit sphere of a real Banach space can be extended to a linear isometry of the entire space.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 10","pages":"Article 111122"},"PeriodicalIF":1.7,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144579256","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}