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Functional Analysis and Its Applications最新文献

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On Quantum Floquet Theorem 论量子Floquet定理
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-04-16 DOI: 10.1134/S1234567825010082
Dmitry Treschev
{"title":"On Quantum Floquet Theorem","authors":"Dmitry Treschev","doi":"10.1134/S1234567825010082","DOIUrl":"10.1134/S1234567825010082","url":null,"abstract":"<p> We consider the Schrödinger equation <span>(ihpartial_tpsi=Hpsi)</span>, <span>(psi=psi(cdot,t)in L^2(mathbb{T}))</span>. The operator <span>(H=-partial^2_x+V(x,t))</span> includes a smooth potential <span>(V)</span>, which is assumed to be time <span>(T)</span>-periodic. Let <span>(W=W(t))</span> be the fundamental solution of this linear ODE system on <span>(L^2(mathbb{T}))</span>. Then, according to the terminology from Lyapunov–Floquet theory, <span>(mathcal M=W(T))</span> is the monodromy operator. We prove that <span>(mathcal M)</span> is unitarily conjugated to <span>(D+mathcal C)</span>, where <span>(D)</span> is diagonal in the standard Fourier basis, while <span>(mathcal C)</span> is a compact operator with an arbitrarily small norm. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 1","pages":"91 - 105"},"PeriodicalIF":0.6,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143840426","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 Interlace Polynomial of Binary Delta-Matroids and Link Invariants 二元三角阵的交错多项式与连杆不变量
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-04-16 DOI: 10.1134/S1234567825010033
Nadezhda Kodaneva
{"title":"The Interlace Polynomial of Binary Delta-Matroids and Link Invariants","authors":"Nadezhda Kodaneva","doi":"10.1134/S1234567825010033","DOIUrl":"10.1134/S1234567825010033","url":null,"abstract":"<p> In this work, we study the interlace polynomial as a generalization of a graph invariant to delta-matroids. We prove that the interlace polynomial satisfies the four-term relation for delta-matroids and thus determines a finite type invariant of links in the <span>(3)</span>-sphere. Using the interlace polynomial, we give a lower bound for the size of the Hopf algebra of binary delta-matroids modulo the <span>(4)</span>-term relations. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 1","pages":"19 - 31"},"PeriodicalIF":0.6,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143840430","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
Fundamental Solutions of Multilinear Differential Operators with Constant Coefficients 常系数多线性微分算子的基本解法
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-04-16 DOI: 10.1134/S1234567825010045
Boris Lidskii
{"title":"Fundamental Solutions of Multilinear Differential Operators with Constant Coefficients","authors":"Boris Lidskii","doi":"10.1134/S1234567825010045","DOIUrl":"10.1134/S1234567825010045","url":null,"abstract":"<p> This paper generalizes part of the author’s previous results. Let <span>(L)</span> be a multilinear differential operator with constant coefficients. The fundamental solution <span>(phi)</span> supported in a convex cone of a linear space <span>(U)</span> is piecewise polynomial. Choose a basis in the space <span>(T)</span> of polynomials and consider the corresponding set of convex cones in the space <span>(U)</span>. We claim that <span>(phi (x))</span> is equal to a sum of basis elements in <span>(T)</span>, with the sum being taken over those elements for which the corresponding cones contain <span>(x)</span>. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 1","pages":"32 - 37"},"PeriodicalIF":0.6,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143840432","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
(Weakly) Almost Periodic Functions and Fixed Point Properties on Norm Separable (*)-Weak Compact Convex Sets in Dual Banach Spaces 对偶Banach空间中模可分(*) -弱紧凸集的（弱）概周期函数和不动点性质
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-04-16 DOI: 10.1134/S1234567825010070
Khadime Salame
{"title":"(Weakly) Almost Periodic Functions and Fixed Point Properties on Norm Separable (*)-Weak Compact Convex Sets in Dual Banach Spaces","authors":"Khadime Salame","doi":"10.1134/S1234567825010070","DOIUrl":"10.1134/S1234567825010070","url":null,"abstract":"<p> Given a semitopological semigroup <span>(S)</span>, let <span>(operatorname{WAP}(S))</span> and <span>(operatorname{AP}(S))</span> be the algebras of weakly and strongly almost periodic functions on <span>(S)</span>, respectively. This paper centers around the study of the fixed point property (<span>(mathbf{F}_{*,s})</span>): whenever <span>(picolon Stimes K to K)</span> is a jointly <span>(*)</span>-weak continuous nonexpansive action on a non-empty norm separable <span>(*)</span>-weak compact convex set <span>(K)</span> in the dual <span>(E^*)</span> of a Banach space <span>(E)</span>, then there is a common fixed point for <span>(S)</span> in <span>(K)</span>. We are primarily interested in answering the following problems posed by Lau and Zhang. (1) Let <span>(S)</span> be a discrete semigroup. If the fixed point property (<span>(mathbf{F}_{*,s})</span>) holds, does <span>(operatorname{WAP}(S))</span> have a left invariant mean? (2) Is the existence of a left invariant mean on <span>(operatorname{WAP}(S))</span> a sufficient condition to ensure the fixed point property (<span>(mathbf{F}_{*,s})</span>)? (3) Do the bicyclic semigroups <span>(S_2=langle e,a,b,c colon ab=ac=erangle)</span> and <span>(S_3=langle e,a,b,c,d colon ac=bd=erangle)</span> have the fixed point property (<span>(mathbf{F}_{*,s})</span>)? Among other things, characterization theorems of the amenability property of the algebras <span>(operatorname{WAP}(S))</span> and <span>(operatorname{AP}(S))</span> are also given. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 1","pages":"79 - 90"},"PeriodicalIF":0.6,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143840429","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 Applicability Condition of a Cutoff Regularization in the Coordinate Representation 坐标表示中截止正则化的适用条件
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-04-16 DOI: 10.1134/S123456782501001X
Aleksandr Ivanov
{"title":"An Applicability Condition of a Cutoff Regularization in the Coordinate Representation","authors":"Aleksandr Ivanov","doi":"10.1134/S123456782501001X","DOIUrl":"10.1134/S123456782501001X","url":null,"abstract":"<p> The paper discusses an applicability condition of a cutoff regularization to a fundamental solution of the Laplace operator in the coordinate representation in the Euclidean space of dimension greater than two. To regularize, we consider a deformation of the solution in a sufficiently small ball centered at the origin by cutting off a singular component, and further supplementing it with a continuous function. It is shown that a set of functions satisfying the applicability condition is not empty. As an example, a family of functions is constructed that can be represented by applying a set of averaging operators to the non-regularized solution, and some specific examples are given. Additionally, it is demonstrated that there exist functions that satisfy the condition in a more strict formulation. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 1","pages":"1 - 10"},"PeriodicalIF":0.6,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143840434","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
Multi-Dimensional Hyperbolic Chaos 多维双曲混沌
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-01-20 DOI: 10.1134/S0016266324040014
Sergey Glyzin, A. Yu. Kolesov
{"title":"Multi-Dimensional Hyperbolic Chaos","authors":"Sergey Glyzin,&nbsp;A. Yu. Kolesov","doi":"10.1134/S0016266324040014","DOIUrl":"10.1134/S0016266324040014","url":null,"abstract":"<p> We propose a mathematical model for a new phenomenon: multi-dimensional hyperbolic chaos. This model is a ring chain of <span>(Nge 2)</span> unidirectionally coupled maps of the two-dimensional torus <span>(mathbb{T}^2)</span>, each of which is of Arnold’s cat map type. We provide sufficient conditions (independent of <span>(N)</span>) under which the chain gives rise to an Anosov diffeomorphism of <span>(mathbb{T}^{2N})</span> for any <span>(Nge 2)</span>. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 4","pages":"349 - 361"},"PeriodicalIF":0.6,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142995319","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 the Differential Operators of Odd Order with (mathrm{PT})-Symmetric Periodic Matrix Coefficients 关于(mathrm{PT}) -对称周期矩阵系数的奇阶微分算子
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-01-20 DOI: 10.1134/S0016266324040099
Oktay Veliev
{"title":"On the Differential Operators of Odd Order with (mathrm{PT})-Symmetric Periodic Matrix Coefficients","authors":"Oktay Veliev","doi":"10.1134/S0016266324040099","DOIUrl":"10.1134/S0016266324040099","url":null,"abstract":"<p> In this paper, we investigate the spectrum of the differential operator <span>(T)</span> generated by an ordinary differential expression of order <span>(n)</span> with <span>(mathrm{PT})</span>-symmertic periodic <span>(mtimes m)</span> matrix coefficients. We prove that if <span>(m)</span> and <span>(n)</span> are odd numbers, then the spectrum of <span>(T)</span> contains all the real line. Note that in standard quantum theory, observable systems must be Hermitian operators, so as to ensure that the spectrum is real. Research on <span>(mathrm{PT})</span>-symmetric quantum theory is based on the observation that the spectrum of a <span>(mathrm{PT})</span>-symmetric non-self-adjoint operator can contain real numbers. In this paper, we discover a large class of <span>(mathrm{PT})</span>-symmetric operators whose spectrum contains all real axes. Moreover, the proof is very short. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 4","pages":"454 - 457"},"PeriodicalIF":0.6,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142995175","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
Twisted Tensor Product, Smooth DG Algebras, and Noncommutative Resolutions of Singular Curves 扭曲张量积，光滑DG代数，奇异曲线的非交换分辨
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-01-20 DOI: 10.1134/S001626632404004X
Dmitri Orlov
{"title":"Twisted Tensor Product, Smooth DG Algebras, and Noncommutative Resolutions of Singular Curves","authors":"Dmitri Orlov","doi":"10.1134/S001626632404004X","DOIUrl":"10.1134/S001626632404004X","url":null,"abstract":"<p> New families of algebras and DG algebras with two simple modules are introduced and described. Using the twisted tensor product operation, we prove that such algebras have finite global dimension, and that the resulting DG algebras are smooth. This description allows us to show that some of these DG algebras determine smooth proper noncommutative curves that provide smooth minimal noncommutative resolutions for singular rational curves. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 4","pages":"384 - 408"},"PeriodicalIF":0.6,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142995320","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
Finite-Zone (mathcal{PT})-Potentials 有限区域(mathcal{PT}) -潜力
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-01-20 DOI: 10.1134/S0016266324040075
Iskander A. Taimanov
{"title":"Finite-Zone (mathcal{PT})-Potentials","authors":"Iskander A. Taimanov","doi":"10.1134/S0016266324040075","DOIUrl":"10.1134/S0016266324040075","url":null,"abstract":"<p> We give a description of finite-zone <span>(mathcal{PT})</span>-potentials in terms of explicit theta-functional formulas. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 4","pages":"438 - 450"},"PeriodicalIF":0.6,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142995203","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’s Theorem on the Precompactness of Subsets of Functional Spaces over Pseudocompact Spaces 伪紧空间上泛函空间子集的预紧性的Grothendieck定理
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-01-20 DOI: 10.1134/S0016266324040051
Evgenii Reznichenko
{"title":"Grothendieck’s Theorem on the Precompactness of Subsets of Functional Spaces over Pseudocompact Spaces","authors":"Evgenii Reznichenko","doi":"10.1134/S0016266324040051","DOIUrl":"10.1134/S0016266324040051","url":null,"abstract":"<p> Generalizations of the theorems of Eberlein and Grothendieck on the precompactness of subsets of function spaces are considered: if <span>(X)</span> is a countably compact space and <span>(C_p(X))</span> is a space of continuous functions on <span>(X)</span> in the topology of pointwise convergence, then any countably compact subspace of the space <span>(C_p(X))</span> is precompact, that is, it has a compact closure. The paper provides an overview of the results on this topic. It is proved that if a pseudocompact <span>(X)</span> contains a dense Lindelöf <span>(Sigma)</span>-space, then pseudocompact subspaces of the space <span>(C_p(X))</span> are precompact. If <span>(X)</span> is the product Čech complete spaces, then bounded subsets of the space <span>(C_p(X))</span> are precompact. Results on the continuity of separately continuous functions are also obtained. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 4","pages":"409 - 426"},"PeriodicalIF":0.6,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142995172","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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