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Functional Analysis and Its Applications最新文献

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On Commuting Differential Operators of Rank 2 Corresponding to Trigonal Spectral Curves of Genus 3 3属三角谱曲线对应的2阶可交换微分算子
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2026-03-31 DOI: 10.1134/S1234567826010088
Matvey Ivlev
{"title":"On Commuting Differential Operators of Rank 2 Corresponding to Trigonal Spectral Curves of Genus 3","authors":"Matvey Ivlev","doi":"10.1134/S1234567826010088","DOIUrl":"10.1134/S1234567826010088","url":null,"abstract":"<p> The construction of ordinary commuting differential operators is a classical problem of differential equations and integrable systems, which has applications in soliton theory. Commuting operators of rank 1 were found by Krichever. The problem of constructing operators of rank <span>(l&gt;1)</span> has not been solved in the general case. In all known examples of operators of rank <span>(l&gt;1)</span>, the spectral curves are hyperelliptic curves. In this paper, the first examples of operators of rank 2, corresponding to trigonal spectral curves of genus 3, are constructed. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"60 1","pages":"102 - 106"},"PeriodicalIF":0.7,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579671","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
On Translation and Dilation Invariant Seminorms 关于平移与扩张不变半精
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2026-03-31 DOI: 10.1134/S1234567826010039
Maxim Romanov
{"title":"On Translation and Dilation Invariant Seminorms","authors":"Maxim Romanov","doi":"10.1134/S1234567826010039","DOIUrl":"10.1134/S1234567826010039","url":null,"abstract":"<p> We consider complete seminormed spaces of functions of one real variable whose seminorm has a finite-dimensional kernel. If the seminorm is invariant under affine changes of the argument, we call such a space interesting. We prove that the maximal interesting space embedded in <span>(L_{1,mathrm{loc}}(mathbb{R}^n))</span> is equivalent to <span>(mathrm{BMO})</span>, and the maximal interesting space embedded in <span>(mathcal{D}'(mathbb{R}))</span> is equivalent to the homogeneous Besov space <span>(dot{B}^0_{infty,infty})</span>. We also construct a minimal interesting space that contains the space of smooth functions with compact support. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"60 1","pages":"34 - 47"},"PeriodicalIF":0.7,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579672","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 Values Assumed by the Weak Homological Bidimension in Certain Classes of Banach Algebras 一类Banach代数的弱同调二维假设值
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2026-03-31 DOI: 10.1134/S1234567826010040
Yurii Selivanov
{"title":"The Values Assumed by the Weak Homological Bidimension in Certain Classes of Banach Algebras","authors":"Yurii Selivanov","doi":"10.1134/S1234567826010040","DOIUrl":"10.1134/S1234567826010040","url":null,"abstract":"<p> Some properties of the weak homological bidimension of Banach algebras are studied and important examples of its calculation are given. In particular, this characteristic is calculated for all semisimple biprojective Banach algebras with the approximation property, all so-called tensor algebras generated by bilinear forms, and all infinite-dimensional Hilbert algebras. In addition, the additivity formula for weak bidimension is proved and it is shown that, in the class of semisimple Banach algebras, this homological characteristic can take any natural values, as well as the values <span>(0)</span> and <span>(infty)</span>. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"60 1","pages":"48 - 72"},"PeriodicalIF":0.7,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579674","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
Shearlet Expansion Theory on Lizorkin-Type Spaces lizorkin型空间上的Shearlet展开理论
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2026-03-31 DOI: 10.1134/S1234567826010064
Astrit R. Ferizi, Katerina Hadzi-Velkova Saneva
{"title":"Shearlet Expansion Theory on Lizorkin-Type Spaces","authors":"Astrit R. Ferizi,&nbsp;Katerina Hadzi-Velkova Saneva","doi":"10.1134/S1234567826010064","DOIUrl":"10.1134/S1234567826010064","url":null,"abstract":"<p> We develop a shearlet expansion theory for the Lizorkin-type spaces <span>(mathcal{S}_{0}(mathbb{R}^2))</span> and <span>(mathcal{S}'_{0}(mathbb{R}^2))</span>. We prove that the shearlet series expansion with respect to a Parseval shearlet converges in the topology of these spaces and provide a topological characterization of the Lizorkin space of distributions in terms of shearlet coefficients. Finally, we apply our distributional shearlet expansion theory to analyze asymptotic properties of distributions and obtain several Tauberian-type results that characterize the quasiasymptotics and quasiasymptotically boundedness of Lizorkin distributions via the asymptotic behavior of their shearlet coefficients. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"60 1","pages":"82 - 96"},"PeriodicalIF":0.7,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579673","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
Kowalski–Słodkowski Theorem for Spectrum Variants Kowalski-Słodkowski谱变分定理
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2026-03-31 DOI: 10.1134/S1234567826010052
Gayathri Sugirtha, Daniel Sukumar
{"title":"Kowalski–Słodkowski Theorem for Spectrum Variants","authors":"Gayathri Sugirtha,&nbsp;Daniel Sukumar","doi":"10.1134/S1234567826010052","DOIUrl":"10.1134/S1234567826010052","url":null,"abstract":"<p> Let <span>(mathcal A)</span> be a complex unital commutative Banach algebra. Let <span>(varphicolon mathcal Ato mathbb C)</span> be a map such that for <span>(x,yinmathcal A)</span>, <span>(varphi(x)-varphi(y)insigma_varepsilon(x-y))</span> and <span>(varphi)</span> has <span>(mathbb C)</span>-linear differentials almost everywhere. Then <span>(varphi)</span> is approximately multiplicative. A similar conclusion is reached by replacing the differential condition with comparable assumptions on the map. This result is similar to the Kowalski–Słodkowski theorem. Analogous versions of it are also discussed for the exponential spectrum and for a particular class of the Ransford spectrum. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"60 1","pages":"73 - 81"},"PeriodicalIF":0.7,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579668","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 Study on the (mathscr{F})-Simultaneous Approximative (tau)-Compactness Property in Banach Spaces Banach空间中(mathscr{F}) -同时逼近(tau) -紧性的研究
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2026-03-31 DOI: 10.1134/S1234567826010015
Syamantak Das, Tanmoy Paul
{"title":"A Study on the (mathscr{F})-Simultaneous Approximative (tau)-Compactness Property in Banach Spaces","authors":"Syamantak Das,&nbsp;Tanmoy Paul","doi":"10.1134/S1234567826010015","DOIUrl":"10.1134/S1234567826010015","url":null,"abstract":"<p> Veselý (1997) studied Banach spaces that admit <span>(f)</span>-centers for finite subsets of the space. In this work, we introduce the concept of the <span>(mathscr{F})</span>-simultaneous approximative <span>(tau)</span>-compactness property (<span>(tau)</span>-<span>(mathscr{F})</span>-<span>(mathrm{SACP})</span> or SACP for short) for triplets <span>((X, V,mathfrak{F}))</span>, where <span>(X)</span> is a Banach space, <span>(V)</span> is a <span>(tau)</span>-closed subset of <span>(X)</span>, <span>(mathfrak{F})</span> is a subfamily of closed and bounded subsets of <span>(X)</span>, <span>(mathscr{F})</span> is a collection of functions, and <span>(tau)</span> is the norm or weak topology on <span>(X)</span>. We characterize reflexive spaces with the Kadec–Klee property using triplets with <span>(tau)</span>-<span>(mathscr{F})</span>-<span>(mathrm{SACP})</span>. We investigate the relationship between <span>(tau)</span>-<span>(mathscr{F})</span>-<span>(mathrm{SACP})</span> and the continuity properties of the restricted <span>(f)</span>-center map. The study further examines <span>(tau)</span>-<span>(mathscr{F})</span>-<span>(mathrm{SACP})</span> in the context of <span>(mathrm{CLUR})</span>-spaces and explores various characterizations of <span>(tau)</span>-<span>(mathscr{F})</span>-<span>(mathrm{SACP})</span>, including connections to reflexivity, Fréchet smoothness, and the Kadec–Klee property. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"60 1","pages":"1 - 13"},"PeriodicalIF":0.7,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579667","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
On Weak Solvability for the Navier–Stokes–Voigt Thermal Model with Nonlinear Viscosity Coefficient 非线性黏度系数Navier-Stokes-Voigt热模型的弱可解性
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2026-03-31 DOI: 10.1134/S1234567826010076
Andrey Zvyagin
{"title":"On Weak Solvability for the Navier–Stokes–Voigt Thermal Model with Nonlinear Viscosity Coefficient","authors":"Andrey Zvyagin","doi":"10.1134/S1234567826010076","DOIUrl":"10.1134/S1234567826010076","url":null,"abstract":"<p> The existence of weak solutions to the initial–boundary value problem for the mathematical model describing the motion of a nonlinearly elastically retarded Navier–Stokes–Voigt fluid is studied in this paper. In this model, the fluid viscosity is considered as a nonlinear function. In addition, the temperature is also taken into account, which leads to the emergence of an additional energy balance equation. The proof is based on the topological approximation approach to the study of hydrodynamic problems, as well as the following iterative process. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"60 1","pages":"97 - 101"},"PeriodicalIF":0.7,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579670","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
Remainders of Continuants with Large Fixed Suffixes 带有大固定后缀的连续词的余数
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2026-03-31 DOI: 10.1134/S1234567826010027
Igor Kan
{"title":"Remainders of Continuants with Large Fixed Suffixes","authors":"Igor Kan","doi":"10.1134/S1234567826010027","DOIUrl":"10.1134/S1234567826010027","url":null,"abstract":"<p> To every finite word of a finite alphabet <span>(mathbf{A}subseteq mathbb{N})</span>, one can add a prefix <span>(V)</span> and a suffix <span>(W)</span> that are fixed finite words of the alphabet <span>(mathbb{N})</span>. The words thus obtained are related to finite continued fraction expansions of certain numbers from <span>((0,1)cap mathbb{Q})</span>. Their irreducible denominators that belong to <span>([1,N])</span> form the set <span>(mathfrak{D}^{N}_{mathbf{A},V,W})</span>. In the author’s previous work, it was shown that, under certain conditions on <span>(mathbf{A})</span> and <span>(Qinmathbb{N})</span>, and provided that the lengths of <span>(V)</span> and <span>(W)</span> are not very large, the set <span>(mathfrak{D}^{N}_{mathbf{A},V,W})</span> contains almost all possible remainders modulo <span>(Q)</span>; moreover, the corresponding formula has power-law decay. In this paper, we obtain an analogous formula for an arbitrarily long suffix <span>(W)</span>. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"60 1","pages":"14 - 33"},"PeriodicalIF":0.7,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579669","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
Minimal Triangulations of Circle Bundles 圆束的最小三角剖分
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2026-01-15 DOI: 10.1134/S1234567825040056
Gaiane Panina, Maksim Turevskii
{"title":"Minimal Triangulations of Circle Bundles","authors":"Gaiane Panina,&nbsp;Maksim Turevskii","doi":"10.1134/S1234567825040056","DOIUrl":"10.1134/S1234567825040056","url":null,"abstract":"<p> A triangulation of a circle bundle <span>(E xrightarrow{pi} B)</span> is a triangulation of the total space <span>(E)</span> and the base <span>(B)</span> such that the projection <span>(pi)</span> is a simplicial map. In the paper, we address the following questions. <i>Which circle bundles can be triangulated over a given triangulation of the base? What are the minimal triangulations of a bundle?</i> A complete solution for semisimplicial triangulations was given by N. Mnëv. Our results deal with classical triangulations, i.e., simplicial complexes. We give an exact answer for an infinite family of triangulated spheres (including the boundary of the <span>(3)</span>-simplex, the boundary of the octahedron, the suspension over an <span>(n)</span>-gon, the icosahedron). For the general case, we present a sufficient condition for the existence of a triangulation. Some minimality results follow straightforwadly. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 4","pages":"430 - 439"},"PeriodicalIF":0.7,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145963729","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
Separating Semigroup of Genus 4 Curves 4曲线属半群的分离
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2026-01-15 DOI: 10.1134/S1234567825040044
Stepan Orevkov
{"title":"Separating Semigroup of Genus 4 Curves","authors":"Stepan Orevkov","doi":"10.1134/S1234567825040044","DOIUrl":"10.1134/S1234567825040044","url":null,"abstract":"<p> A rational function on a real algebraic curve <span>(C)</span> is called separating if it takes real values only at real points. Such a function defines a covering <span>(mathbb R Ctomathbb{RP}^1)</span>. Let <span>(c_1,dots,c_r)</span> be the connected components of <span>(mathbb R C)</span>. M. Kummer and K. Shaw defined the separating semigroup of <span>(C)</span> as the set of all sequences <span>((d_1(f),dots,d_r(f)))</span> where <span>(f)</span> is a separating function, and <span>(d_i(f))</span> is the degree of the restriction of <span>(f)</span> to <span>(c_i)</span>. </p><p> In the present paper, we describe the separating semigroups of all genus 4 curves. For the proofs, we consider the canonical embedding of <span>(C)</span> into a quadric <span>(X)</span> in <span>(mathbb P^3)</span>, and apply Abel’s theorem to 1-forms on <span>(C)</span> obtained as Poincaré residues of certain meromorphic 2-forms. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 4","pages":"421 - 429"},"PeriodicalIF":0.7,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145963680","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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