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Functional Analysis and Its Applications最新文献

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The Mumford Dynamical System and the Gelfand–Dikii Recursion 芒福德动力系统和格尔芬-迪基递归
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-04-01 DOI: 10.1134/S0016266323040020
P. G. Baron
{"title":"The Mumford Dynamical System and the Gelfand–Dikii Recursion","authors":"P. G. Baron","doi":"10.1134/S0016266323040020","DOIUrl":"10.1134/S0016266323040020","url":null,"abstract":"<p> In his paper “The Mumford dynamical system and hyperelliptic Kleinian functions” [Funkts. Anal. Prilozhen. <b>57</b> (4), 27–45 (2023)] Victor Buchstaber developed the differential-algebraic theory of the Mumford dynamical system. The key object of this theory is the <span>((P,Q))</span>-recursion introduced in his paper. </p><p> In the present paper, we further develop the theory of the <span>((P,Q))</span>-recursion and describe its connections to the Korteweg–de Vries hierarchy, the Lenard operator, and the Gelfand–Dikii recursion. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 4","pages":"279 - 287"},"PeriodicalIF":0.6,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140590307","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
Classification of Measurable Functions of Several Variables and Matrix Distributions 多变量可测量函数和矩阵分布的分类
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-04-01 DOI: 10.1134/S0016266323040044
A. M. Vershik
{"title":"Classification of Measurable Functions of Several Variables and Matrix Distributions","authors":"A. M. Vershik","doi":"10.1134/S0016266323040044","DOIUrl":"10.1134/S0016266323040044","url":null,"abstract":"<p> We consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the one hand, this is an invariant of this function with respect to a certain group of transformations of variables; on the other hand, this is a special probability measure in the space of matrices (tensors) that is invariant under actions of natural infinite permutation groups. The intricate interplay of both interpretations of matrix (tensor) distributions makes them an important subject of modern functional analysis. We formulate and prove a theorem that, under certain conditions on a measurable function of two variables, its matrix distribution is a complete invariant. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 4","pages":"303 - 313"},"PeriodicalIF":0.6,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140590230","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
Self-Joinings and Generic Extensions of Ergodic Systems Ergodic 系统的自连接和通用扩展
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-03-12 DOI: 10.1134/S0016266323030048
V. V. Ryzhikov
{"title":"Self-Joinings and Generic Extensions of Ergodic Systems","authors":"V. V. Ryzhikov","doi":"10.1134/S0016266323030048","DOIUrl":"10.1134/S0016266323030048","url":null,"abstract":"<p> It is proved that the generic extensions of a dynamical system inherit the triviality of pairwise independent self-joinings. This property is related to well-known problems of joining theory and to Rokhlin’s famous multiple mixing problem. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 3","pages":"236 - 247"},"PeriodicalIF":0.6,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140128282","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
Linear and Multiplicative Maps under Spectral Conditions 谱条件下的线性和乘法映射
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-03-12 DOI: 10.1134/S0016266323030012
Bhumi Amin, Ramesh Golla
{"title":"Linear and Multiplicative Maps under Spectral Conditions","authors":"Bhumi Amin,&nbsp;Ramesh Golla","doi":"10.1134/S0016266323030012","DOIUrl":"10.1134/S0016266323030012","url":null,"abstract":"<p> The multiplicative version of the Gleason–Kahane–Żelazko theorem for <span>(C^*)</span>-algebras given by Brits et al. in [4] is extended to maps from <span>(C^*)</span>-algebras to commutative semisimple Banach algebras. In particular, it is proved that if a multiplicative map <span>(phi)</span> from a <span>(C^*)</span>-algebra <span>(mathcal{U})</span> to a commutative semisimple Banach algebra <span>(mathcal{V})</span> is continuous on the set of all noninvertible elements of <span>(mathcal{U})</span> and <span>(sigma(phi(a)) subseteq sigma(a))</span> for any <span>(a in mathcal{U})</span>, then <span>(phi)</span> is a linear map. The multiplicative variation of the Kowalski–Słodkowski theorem given by Touré et al. in [14] is also generalized. Specifically, if <span>(phi)</span> is a continuous map from a <span>(C^*)</span>-algebra <span>(mathcal{U})</span> to a commutative semisimple Banach algebra <span>(mathcal{V})</span> satisfying the conditions <span>(phi(1_mathcal{U})=1_mathcal{V})</span> and <span>(sigma(phi(x)phi(y)) subseteq sigma(xy))</span> for all <span>(x,y in mathcal{U})</span>, then <span>(phi)</span> generates a linear multiplicative map <span>(gamma_phi)</span> on <span>(mathcal{U})</span> which coincides with <span>(phi)</span> on the principal component of the invertible group of <span>(mathcal{U})</span>. If <span>(mathcal{U})</span> is a Banach algebra such that each element of <span>(mathcal{U})</span> has totally disconnected spectrum, then the map <span>(phi)</span> itself is linear and multiplicative on <span>(mathcal{U})</span>. It is shown that a similar statement is valid for a map with semisimple domain under a stricter spectral condition. Examples which demonstrate that some hypothesis in the results cannot be discarded. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 3","pages":"179 - 191"},"PeriodicalIF":0.6,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140128333","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
Two-Dimensional Diffusion Orthogonal Polynomials Ordered by a Weighted Degree 按加权度排序的二维扩散正交多项式
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-03-12 DOI: 10.1134/S0016266323030036
S. Yu. Orevkov
{"title":"Two-Dimensional Diffusion Orthogonal Polynomials Ordered by a Weighted Degree","authors":"S. Yu. Orevkov","doi":"10.1134/S0016266323030036","DOIUrl":"10.1134/S0016266323030036","url":null,"abstract":"<p> We study the problem of describing the triples <span>((Omega,g,mu))</span>, <span>(mu=rho,dx)</span>, where <span>(g= (g^{ij}(x)))</span> is the (co)metric associated with a symmetric second-order differential operator <span>(mathbf{L}(f) = frac{1}{rho}sum_{ij} partial_i (g^{ij} rho,partial_j f))</span> defined on a domain <span>(Omega)</span> of <span>(mathbb{R}^d)</span> and such that there exists an orthonormal basis of <span>(mathcal{L}^2(mu))</span> consisting of polynomials which are eigenvectors of <span>(mathbf{L})</span> and this basis is compatible with the filtration of the space of polynomials by some weighted degree. </p><p> In a joint paper of D. Bakry, M. Zani, and the author this problem was solved in dimension 2 for the usual degree. In the present paper we solve it still in dimension 2 but for a weighted degree with arbitrary positive weights. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 3","pages":"208 - 235"},"PeriodicalIF":0.6,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140128265","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
Resurgence and Partial Theta Series 复活和部分 Theta 系列
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-03-12 DOI: 10.1134/S001626632303005X
Li Han, Yong Li, David Sauzin, Shanzhong Sun
{"title":"Resurgence and Partial Theta Series","authors":"Li Han,&nbsp;Yong Li,&nbsp;David Sauzin,&nbsp;Shanzhong Sun","doi":"10.1134/S001626632303005X","DOIUrl":"10.1134/S001626632303005X","url":null,"abstract":"<p> We consider partial theta series associated with periodic sequences of coefficients, namely, <span>(Theta(tau):= sum_{n&gt;0} n^nu f(n) e^{ipi n^2tau/M})</span>, where <span>(nuinmathbb{Z}_{ge0})</span> and </p><p> <span>(fcolonmathbb{Z} to mathbb{C})</span> is an <span>(M)</span>-periodic function. Such a function <span>(Theta)</span> is analytic in the half-plane <span>({ operatorname {Im}tau&gt;0})</span> and in the asymptotics of <span>(Theta(tau))</span> as <span>(tau)</span> tends nontangentially to any <span>(alphainmathbb{Q})</span> a formal power series appears, which depends on the parity of <span>(nu)</span> and <span>(f)</span>. We discuss the summability and resurgence properties of these series; namely, we present explicit formulas for their formal Borel transforms and their consequences for the modularity properties of <span>(Theta)</span>, or its “quantum modularity” properties in the sense of Zagier’s recent theory. The discrete Fourier transform of <span>(f)</span> plays an unexpected role and leads to a number-theoretic analogue of Écalle’s “bridge equations.” The main thesis is: (quantum) modularity <span>(=)</span> Stokes phenomenon <span>(+)</span> discrete Fourier transform. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 3","pages":"248 - 265"},"PeriodicalIF":0.6,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140128269","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
Resolution of Singularities of the Odd Nilpotent Cone of Orthosymplectic Lie Superalgebras 正交列超拉的奇数无势锥的奇点解析
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2024-03-12 DOI: 10.1134/S0016266323030024
I. D. Motorin
{"title":"Resolution of Singularities of the Odd Nilpotent Cone of Orthosymplectic Lie Superalgebras","authors":"I. D. Motorin","doi":"10.1134/S0016266323030024","DOIUrl":"10.1134/S0016266323030024","url":null,"abstract":"<p> We construct a Springer-type resolution of singularities of the odd nilpotent cone of the orthosymplectic Lie superalgebras <span>(mathfrak{osp}(m|2n))</span>. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 3","pages":"192 - 207"},"PeriodicalIF":0.6,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140128334","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 Convergence Rate Estimate for Remotest Projections on Three Subspaces 三个子空间上最远投影的收敛率估算
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-12-29 DOI: 10.1134/S0016266323020077
P. A. Borodin, L. Sh. Burusheva
{"title":"A Convergence Rate Estimate for Remotest Projections on Three Subspaces","authors":"P. A. Borodin,&nbsp;L. Sh. Burusheva","doi":"10.1134/S0016266323020077","DOIUrl":"10.1134/S0016266323020077","url":null,"abstract":"<p> We give an estimate of the rate of convergence to zero of the norms of remotest projections on three subspaces of a Hilbert space with zero intersection for starting vectors in the sum of orthogonal complements to these subspaces. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 2","pages":"164 - 168"},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139069408","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
Limit Spectral Measures of Matrix Distributions of Metric Triples 度量三元矩阵分布的极限谱量
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-12-29 DOI: 10.1134/S0016266323020089
A. M. Vershik, F. V. Petrov
{"title":"Limit Spectral Measures of Matrix Distributions of Metric Triples","authors":"A. M. Vershik,&nbsp;F. V. Petrov","doi":"10.1134/S0016266323020089","DOIUrl":"10.1134/S0016266323020089","url":null,"abstract":"<p> The notion of the limit spectral measure of a metric triple (i.e., a metric measure space) is defined. If the metric is square integrable, then the limit spectral measure is deterministic and coincides with the spectrum of the integral operator on <span>(L^2(mu))</span> with kernel <span>(rho)</span>. An example in which there is no deterministic spectral measure is constructed. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 2","pages":"169 - 172"},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139069351","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
The Quasilinear Parabolic Venttsel’ Problem with Discontinuous Leading Coefficients 前导系数不连续的准线性抛物线文特塞尔问题
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-12-29 DOI: 10.1134/S0016266323020065
D. E. Apushkinskaya, A. I. Nazarov, D. K. Palagachev, L. G. Softova
{"title":"The Quasilinear Parabolic Venttsel’ Problem with Discontinuous Leading Coefficients","authors":"D. E. Apushkinskaya,&nbsp;A. I. Nazarov,&nbsp;D. K. Palagachev,&nbsp;L. G. Softova","doi":"10.1134/S0016266323020065","DOIUrl":"10.1134/S0016266323020065","url":null,"abstract":"<p> New results on the strong solvability in Sobolev spaces of the quasilinear Venttsel’ problem for parabolic equations with discontinuous leading coefficients are obtained. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 2","pages":"158 - 163"},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139069352","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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