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Functional Analysis and Its Applications最新文献

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Combinatorial Results Implied by Many Zero Divisors in a Group Ring 群环中许多零除数所隐含的组合结果
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-05-16 DOI: 10.1134/S0016266324010076
Fedor Petrov
{"title":"Combinatorial Results Implied by Many Zero Divisors in a Group Ring","authors":"Fedor Petrov","doi":"10.1134/S0016266324010076","DOIUrl":"10.1134/S0016266324010076","url":null,"abstract":"<p> In a paper of Croot, Lev and Pach and a later paper of Ellenberg and Gijswijt, it was proved that for a group <span>(G=G_0^n)</span>, where <span>(G_0ne {1,-1}^m)</span> is a fixed finite Abelian group and <span>(n)</span> is large, any subset <span>(Asubset G)</span> without 3-progressions (triples <span>(x)</span>, <span>(y)</span>, <span>(z)</span> of different elements with <span>(xy=z^2)</span>) contains at most <span>(|G|^{1-c})</span> elements, where <span>(c&gt;0)</span> is a constant depending only on <span>(G_0)</span>. This is known to be false when <span>(G)</span> is, say, a large cyclic group. The aim of this note is to show that the algebraic property corresponding to this difference is the following: in the first case, a group algebra <span>(mathbb{F}[G])</span> over a suitable field <span>(mathbb{F})</span> contains a subspace <span>(X)</span> with codimension at most <span>(|X|^{1-c})</span> such that <span>(X^3=0)</span>. We discuss which bounds are obtained for finite Abelian <span>(p)</span>-groups and for some matrix <span>(p)</span>-groups: the Heisenberg group over <span>(mathbb{F}_p)</span> and the unitriangular group over <span>(mathbb{F}_p)</span>. We also show how the method allows us to generalize the results of [14] and [12]. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 1","pages":"80 - 89"},"PeriodicalIF":0.6,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141063622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Noncommutative Geometry of Random Surfaces 随机曲面的非交换几何学
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-05-16 DOI: 10.1134/S0016266324010064
Andrei Okounkov
{"title":"Noncommutative Geometry of Random Surfaces","authors":"Andrei Okounkov","doi":"10.1134/S0016266324010064","DOIUrl":"10.1134/S0016266324010064","url":null,"abstract":"<p> We associate a noncommutative curve to a periodic, bipartite, planar dimer model with polygonal boundary. It determines the inverse Kasteleyn matrix and hence all correlations. It may be seen as a quantization of the limit shape construction of Kenyon and the author. We also discuss various directions in which this correspondence may be generalized. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 1","pages":"65 - 79"},"PeriodicalIF":0.6,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S0016266324010064.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141063665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Compactification of Spaces of Measures 论度量空间的紧凑性
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-05-16 DOI: 10.1134/S0016266324010027
Vladimir Bogachev
{"title":"On Compactification of Spaces of Measures","authors":"Vladimir Bogachev","doi":"10.1134/S0016266324010027","DOIUrl":"10.1134/S0016266324010027","url":null,"abstract":"<p> In this paper, we compare the Stone–Čech compactification <span>(beta mathcal{P}(X))</span> of the space <span>(mathcal{P}(X))</span> of Radon probability measures on a Tychonoff space <span>(X)</span>, equipped with the weak topology, with the space <span>(mathcal{P}(beta X))</span> of Radon probability measures on the Stone–Čech compactification <span>(beta X)</span> of the space <span>(X)</span>. It is shown that for any noncompact metric space <span>(X)</span>, the compactification <span>(beta mathcal{P}(X))</span> does not coincide with <span>(mathcal{P}(beta X))</span>. We discuss the case of more general Tychonoff spaces and also the case of the Samuel compactification, for which the coincidence holds. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 1","pages":"2 - 15"},"PeriodicalIF":0.6,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141063621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Interior Points of Convex Compact and Continuous Selections of Exact Measures 精确测量的凸紧凑和连续选择的内点
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-05-16 DOI: 10.1134/S001626632401009X
Pavel Semenov
{"title":"Interior Points of Convex Compact and Continuous Selections of Exact Measures","authors":"Pavel Semenov","doi":"10.1134/S001626632401009X","DOIUrl":"10.1134/S001626632401009X","url":null,"abstract":"<p> For a metric space <span>(M)</span>, we prove existence of continuous maps <span>({M_n}^{infty}_{n=1})</span> associating to each compact set <span>(K subset M)</span>, a probability measure <span>(M_n(K))</span> with <span>(operatorname{supp}(M_n(K)) = K)</span> in such a way that the set <span>({M_n(K)}^{infty}_{n=1})</span> is dense in the space of probability measures on <span>(K)</span>. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 1","pages":"97 - 102"},"PeriodicalIF":0.6,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141063623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Anatoly Moiseevich Vershik. On the occasion of the 90th anniversary 阿纳托利-莫伊谢耶维奇-维尔希克90 周年之际
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-05-16 DOI: 10.1134/S0016266324010015
Editorial Board
{"title":"Anatoly Moiseevich Vershik. On the occasion of the 90th anniversary","authors":"Editorial Board","doi":"10.1134/S0016266324010015","DOIUrl":"10.1134/S0016266324010015","url":null,"abstract":"","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 1","pages":"1 - 1"},"PeriodicalIF":0.6,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Quasi-Similarity, Entropy and Disjointness of Ergodic Actions Ergodic Actions 的准相似性、熵和不邻接性
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-05-16 DOI: 10.1134/S0016266324010088
Valerii Ryzhikov, Jean-Paul Thouvenot
{"title":"Quasi-Similarity, Entropy and Disjointness of Ergodic Actions","authors":"Valerii Ryzhikov,&nbsp;Jean-Paul Thouvenot","doi":"10.1134/S0016266324010088","DOIUrl":"10.1134/S0016266324010088","url":null,"abstract":"<p> We answer a question posed by Vershik regarding connections between quasi-similarity of dynamical systems and Kolmogorov entropy. We prove that all Bernoulli actions of a given countably infinite group are quasi-similar to each other. The existence of non-Bernoulli actions in the same quasi-similarity class is an open problem. A notion opposite to quasi-similarity is that of disjointness (or independence) of actions. Pinsker proved that a deterministic action is independent from an action with completely positive entropy. Using joinings, we obtain the following generalization of Pinsker’s theorem: an action with zero <span>(P)</span>-entropy (an invariant defined by Kirillov and Kushnirenko) and an action with completely positive <span>(P)</span>-entropy are disjoint. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 1","pages":"90 - 96"},"PeriodicalIF":0.6,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141063910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A Convex-Block Approach to Numerical Radius Inequalities 数值半径不等式的凸块方法
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-04-30 DOI: 10.1134/S0016266323050039
Mohammad Sababheh, Cristian Conde, Hamid Reza Moradi
{"title":"A Convex-Block Approach to Numerical Radius Inequalities","authors":"Mohammad Sababheh,&nbsp;Cristian Conde,&nbsp;Hamid Reza Moradi","doi":"10.1134/S0016266323050039","DOIUrl":"10.1134/S0016266323050039","url":null,"abstract":"<p> A simple convex approach and block techniques are used to obtain new sharpened versions of numerical radius inequalities for Hilbert space operators. These include comparisons of norms of operators, their Cartesian parts, their numerical radii, and the numerical radius of the product of two operators. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 1 supplement","pages":"26 - 30"},"PeriodicalIF":0.6,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140830387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
An Index Theorem for Linear Relations and Its Applications to the Study of Block Relation Matrices 线性关系索引定理及其在块关系矩阵研究中的应用
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-04-30 DOI: 10.1134/S0016266323050015
Ayoub Ghorbel, Maher Mnif
{"title":"An Index Theorem for Linear Relations and Its Applications to the Study of Block Relation Matrices","authors":"Ayoub Ghorbel,&nbsp;Maher Mnif","doi":"10.1134/S0016266323050015","DOIUrl":"10.1134/S0016266323050015","url":null,"abstract":"<p> In this paper, we aim to prove an index theorem for linear relations and apply it to study the invertibility and the essential invertibility of certain upper triangular block relation matrices. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 1 supplement","pages":"1 - 16"},"PeriodicalIF":0.6,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140830256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Spectral Inclusion Properties of Quaternionic Krein Space Numerical Range 四元克雷因空间数值范围的频谱包容特性
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-04-30 DOI: 10.1134/S0016266323050027
Kamel Mahfoudhi
{"title":"Spectral Inclusion Properties of Quaternionic Krein Space Numerical Range","authors":"Kamel Mahfoudhi","doi":"10.1134/S0016266323050027","DOIUrl":"10.1134/S0016266323050027","url":null,"abstract":"<p> The article provides a concise overview of key concepts related to right quaternionic linear operators, quaternionic Hilbert spaces, and quaternionic Krein spaces. It then delves into the study of the quaternionic Krein space numerical range of a bounded right linear operator and the relationship between this numerical range and the <span>(S)</span>-spectrum of the operator. The article concludes by establishing spectral inclusion results based on the quaternionic Krein space numerical range and presenting the corresponding spectral inclusion theorems. In addition, we generalize some results to infinite dimensional quaternionic Krein spaces and give some examples. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 1 supplement","pages":"17 - 25"},"PeriodicalIF":0.6,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140830301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Homogenization of Hyperbolic Equations: Operator Estimates with Correctors Taken into Account 双曲方程的均质化：考虑校正器的算子估算
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-04-01 DOI: 10.1134/S0016266323040093
M. A. Dorodnyi, T. A. Suslina
{"title":"Homogenization of Hyperbolic Equations: Operator Estimates with Correctors Taken into Account","authors":"M. A. Dorodnyi,&nbsp;T. A. Suslina","doi":"10.1134/S0016266323040093","DOIUrl":"10.1134/S0016266323040093","url":null,"abstract":"<p> An elliptic second-order differential operator <span>(A_varepsilon=b(mathbf{D})^*g(mathbf{x}/varepsilon)b(mathbf{D}))</span> on <span>(L_2(mathbb{R}^d))</span> is considered, where <span>(varepsilon &gt;0)</span>, <span>(g(mathbf{x}))</span> is a positive definite and bounded matrix-valued function periodic with respect to some lattice, and <span>(b(mathbf{D}))</span> is a matrix first-order differential operator. Approximations for small <span>(varepsilon)</span> of the operator-functions <span>(cos(tau A_varepsilon^{1/2}))</span> and <span>(A_varepsilon^{-1/2} sin (tau A_varepsilon^{1/2}))</span> in various operator norms are obtained. The results can be applied to study the behavior of the solution of the Cauchy problem for the hyperbolic equation <span>(partial^2_tau mathbf{u}_varepsilon(mathbf{x},tau) = - A_varepsilon mathbf{u}_varepsilon(mathbf{x},tau))</span>. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 4","pages":"364 - 370"},"PeriodicalIF":0.6,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140590251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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