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Functional Analysis and Its Applications最新文献

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Elliptic Analogue of the Vershik–Kerov Limit Shape Vershik-Kerov 极限形状的椭圆类似物
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-07-21 DOI: 10.1134/S0016266324020059
Andrei Grekov, Nikita Nekrasov
{"title":"Elliptic Analogue of the Vershik–Kerov Limit Shape","authors":"Andrei Grekov,&nbsp;Nikita Nekrasov","doi":"10.1134/S0016266324020059","DOIUrl":"10.1134/S0016266324020059","url":null,"abstract":"<p> We review the limit shape problem for the Plancherel measure and its generalizations found in supersymmetric gauge theory instanton count. We focus on the measure, interpolating between the Plancherel measure and the uniform measure, a <span>(U(1))</span> case of <span>(mathcal{N}=2^{*})</span> gauge theory. We give the formula for its limit shape in terms of elliptic functions, generalizing the trigonometric “arcsin” law of Vershik–Kerov and Logan–Schepp. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 2","pages":"143 - 159"},"PeriodicalIF":0.6,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S0016266324020059.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740761","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
Anatoly Moiseevich Vershik (1933–2024) 阿纳托利-莫伊谢耶维奇-韦尔希克（1933-2024）
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-07-21 DOI: 10.1134/S0016266324020011
Editorial Board
{"title":"Anatoly Moiseevich Vershik (1933–2024)","authors":"Editorial Board","doi":"10.1134/S0016266324020011","DOIUrl":"10.1134/S0016266324020011","url":null,"abstract":"","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 2","pages":"103 - 104"},"PeriodicalIF":0.6,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740757","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
Duality for the Kantorovich Problem with a Fixed Barycenter and Barycenters of Functionals 具有固定边心和函数边心的康托洛维奇问题的对偶性
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-07-21 DOI: 10.1134/S0016266324020023
Konstantin Afonin
{"title":"Duality for the Kantorovich Problem with a Fixed Barycenter and Barycenters of Functionals","authors":"Konstantin Afonin","doi":"10.1134/S0016266324020023","DOIUrl":"10.1134/S0016266324020023","url":null,"abstract":"<p> The paper is devoted to the study of duality in the linear Kantorovich problem with a fixed barycenter. It is proved that Kantorovich duality holds for general lower semicontinuous cost functions on completely regular spaces. In the course of considering this subject, the question of representation of a continuous linear functional by a Radon measure is raised and solved, provided that the barycenter of the functional is given by a Radon measure. In addition, we consider two new barycentric optimization problems and prove duality results for them. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 2","pages":"105 - 119"},"PeriodicalIF":0.6,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740758","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
Grothendieck Ring of Pairs of Quasi-Projective Varieties 准投影变项对的格罗根迪克环
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-05-16 DOI: 10.1134/S0016266324010040
Sabir Gusein-Zade, Ignacio Luengo, Alejandro Melle-Hernández
{"title":"Grothendieck Ring of Pairs of Quasi-Projective Varieties","authors":"Sabir Gusein-Zade,&nbsp;Ignacio Luengo,&nbsp;Alejandro Melle-Hernández","doi":"10.1134/S0016266324010040","DOIUrl":"10.1134/S0016266324010040","url":null,"abstract":"<p> We define a Grothendieck ring of pairs of complex quasi-projective varieties (consisting of a variety and a subvariety). We describe <span>(lambda)</span>-structures on this ring and a power structure over it. We show that the conjectual symmetric power of the projective line with several orbifold points described by A. Fonarev is consistent with the symmetric power of this line with the set of distinguished points as a pair of varieties. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 1","pages":"33 - 38"},"PeriodicalIF":0.6,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141063624","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
Intrinsic Ergodicity, Generators, and Symbolic Representations of Algebraic Group Actions 代数群作用的本征遍历性、生成器和符号表示
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-05-16 DOI: 10.1134/S0016266324010052
Hanfeng Li, Klaus Schmidt
{"title":"Intrinsic Ergodicity, Generators, and Symbolic Representations of Algebraic Group Actions","authors":"Hanfeng Li,&nbsp;Klaus Schmidt","doi":"10.1134/S0016266324010052","DOIUrl":"10.1134/S0016266324010052","url":null,"abstract":"<p> We construct natural symbolic representations of intrinsically ergodic, but not necessarily expansive, principal algebraic actions of countably infinite amenable groups and use these representations to find explicit generating partitions (up to null-sets) for such actions. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 1","pages":"39 - 64"},"PeriodicalIF":0.6,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141063580","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
Polynomial Eulerian Characteristic of Nilmanifolds Nilmanifolds 的多项式欧拉特征
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-05-16 DOI: 10.1134/S0016266324010039
Victor Bukhshtaber
{"title":"Polynomial Eulerian Characteristic of Nilmanifolds","authors":"Victor Bukhshtaber","doi":"10.1134/S0016266324010039","DOIUrl":"10.1134/S0016266324010039","url":null,"abstract":"<p> The article studies bundle towers <span>(M^{n+1}to M^{n}to dots to S^1)</span>, <span>(geqslant 1)</span>, with fiber <span>(S^1)</span>, where <span>(M^n = L^n!/Gamma^n)</span> are compact smooth nilmanifolds and <span>(L^nthickapprox mathbb{R}^n)</span> is a group of polynomial transformations of the line <span>(mathbb{R}^1)</span>. The focus is on the well-known problem of calculating cohomology rings with rational coefficients of manifolds <span>(M^n)</span>. Using the canonical bigradation in the de Rham complex of manifolds <span>(M^n)</span>, we introduce the concept of polynomial Eulerian characteristic and calculate it for these manifolds. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 1","pages":"16 - 32"},"PeriodicalIF":0.6,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141063581","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
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
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