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Functional Analysis and Its Applications最新文献

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The Speed of Convergence Under the Kolmogorov–Smirnov Metric in the Soshnikov Central Limit Theorem for the Sine Process Soshnikov中心极限定理下正弦过程在Kolmogorov-Smirnov度量下的收敛速度
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-07-04 DOI: 10.1134/S1234567825020028
Alexander Bufetov
{"title":"The Speed of Convergence Under the Kolmogorov–Smirnov Metric in the Soshnikov Central Limit Theorem for the Sine Process","authors":"Alexander Bufetov","doi":"10.1134/S1234567825020028","DOIUrl":"10.1134/S1234567825020028","url":null,"abstract":"<p> For rescaled additive functionals of the sine process, upper bounds are obtained for their speed of convergence to the Gaussian distribution with respect to the Kolmogorov–Smirnov metric. Under scaling with coefficient <span>(R&gt;1)</span>, the Kolmogorov–Smirnov distance is bounded from above by <span>(c/log R)</span> for a smooth function, and by <span>(c/R)</span> for a function holomorphic in a horizontal strip. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 2","pages":"114 - 118"},"PeriodicalIF":0.7,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160519","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 Spectrum of the Differential Operators of Odd Order with (mathcal{PT})-Symmetric Coefficients 关于(mathcal{PT}) -对称系数奇阶微分算子的谱
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-07-04 DOI: 10.1134/S123456782502003X
Oktay Veliev
{"title":"On the Spectrum of the Differential Operators of Odd Order with (mathcal{PT})-Symmetric Coefficients","authors":"Oktay Veliev","doi":"10.1134/S123456782502003X","DOIUrl":"10.1134/S123456782502003X","url":null,"abstract":"<p> In this paper, we consider the Bloch eigenvalues and spectrum of the non-self-adjoint differential operator <span>(L)</span> generated by the differential expression of odd order <span>(n)</span> with periodic <span>(mathcal{PT})</span>-symmetric coefficients, where <span>(n&gt;1)</span>. We study the localizations of the Bloch eigenvalues and the structure of the spectrum. Moreover, we find conditions on the norm of the coefficients under which the spectrum of <span>(L)</span> is purely real and coincides with the real line. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 2","pages":"119 - 125"},"PeriodicalIF":0.7,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161918","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 Amount of Nondegenerate Tubular Orbits of 7-Dimensional Lie Algebras in (mathbb C^4) 关于7维李代数的非简并管状轨道的数量 (mathbb C^4)
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-07-04 DOI: 10.1134/S1234567825020065
Valeria Kaverina, Alexander Loboda
{"title":"On the Amount of Nondegenerate Tubular Orbits of 7-Dimensional Lie Algebras in (mathbb C^4)","authors":"Valeria Kaverina,&nbsp;Alexander Loboda","doi":"10.1134/S1234567825020065","DOIUrl":"10.1134/S1234567825020065","url":null,"abstract":"<p> We consider holomorphic realizations in <span>(mathbb C^4)</span> for a large family of 7-dimensional Lie algebras containing a 6-dimensional nilradical and one or two 4-dimensional abelian subalgebras. We show that for these Lie algebras, a natural condition of having tubular Levi-nondegenerate 7-dimensional orbits is rarely compatible with a straightened basis of one of the abelian subalgebras. In many cases, this incompatibility follows easily from the structure and properties of abelian ideals in 4-dimensional subalgebras of the algebras in question. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 2","pages":"159 - 164"},"PeriodicalIF":0.7,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161915","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
Tensor Factorizations of a Unitary Operator with Simple Lebesgue Spectrum 具有简单勒贝格谱的酉算子的张量分解
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-07-04 DOI: 10.1134/S1234567825020090
Valerii Ryzhikov
{"title":"Tensor Factorizations of a Unitary Operator with Simple Lebesgue Spectrum","authors":"Valerii Ryzhikov","doi":"10.1134/S1234567825020090","DOIUrl":"10.1134/S1234567825020090","url":null,"abstract":"<p> We show that for all <span>(n,p&gt;1)</span>, there exists a unitary operator <span>(U)</span> such that the tensor product <span>(Uotimes U^potimesdotsotimes U^{p^{n-1}})</span> is a unitary operator with simple Lebesgue spectrum. Moreover, there exists an ergodic automorphism <span>(T)</span> such that the spectrum of <span>(Todot T)</span> is simple, while the spectrum of <span>(Totimes Totimes T)</span> is absolutely continuous. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 2","pages":"218 - 220"},"PeriodicalIF":0.7,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161917","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
Boundary Classes of Non-Compact Riemannian Manifolds and Perron’s Method 非紧黎曼流形的边界类与Perron方法
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-07-04 DOI: 10.1134/S1234567825020077
Alexander Kondrashov
{"title":"Boundary Classes of Non-Compact Riemannian Manifolds and Perron’s Method","authors":"Alexander Kondrashov","doi":"10.1134/S1234567825020077","DOIUrl":"10.1134/S1234567825020077","url":null,"abstract":"<p> In the present work, we consider solvability of the generalized Dirichlet problem for the linear elliptic differential equation <span>(Lu=f)</span>, where <span>(L=Delta +langle B(x),nablarangle+c(x))</span> is a linear operator, (<span>(B(x))</span> is a vector field of class <span>(mathrm{C}(mathcal{M}))</span>, <span>(c(x)leq0)</span>, <span>(c(x)in mathrm{C}(mathcal{M}))</span>), considered on a non-compact Riemannian manifold <span>((mathcal{M},g))</span>. We develop the approach to this problem, based on equivalence classes, introduced by E. A. Mazepa, which allows to state the problem on non-compact manifolds in the absence of a natural geometric compactification. We introduce and study linear spaces <span>(mathrm{CM}_b)</span> and <span>(mathrm{CM})</span> of such classes. We give a version of the well-known Perron’s method with boundary data in these classes, and establish signs of <span>(L)</span>-parabolicity and <span>(L)</span>-hyperbolicity of the ends of the manifold <span>(mathcal{M})</span> depending on their geometric structure. The signs of hyperbolicity of a manifold play a key role in justifying solvability of the Dirichlet problem, while signs of parabolicity are important for establishing theorems of Liouville type for the manifold. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 2","pages":"165 - 193"},"PeriodicalIF":0.7,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161506","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 Note on Lattice Knots 关于格子结的注释
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-07-04 DOI: 10.1134/S1234567825020016
Sasha Anan’in, Alexandre Grishkov, Dmitrii Korshunov
{"title":"A Note on Lattice Knots","authors":"Sasha Anan’in,&nbsp;Alexandre Grishkov,&nbsp;Dmitrii Korshunov","doi":"10.1134/S1234567825020016","DOIUrl":"10.1134/S1234567825020016","url":null,"abstract":"<p> The aim of this note is to share the observation that the set of elementary operations of Turing on lattice knots can be reduced to just one type of simple local switches. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 2","pages":"107 - 113"},"PeriodicalIF":0.7,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161916","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 Field Analogue of the Elliptic Spin Calogero–Moser Model: Lax Pair and Equations of Motion 椭圆自旋Calogero-Moser模型的场模拟：Lax对和运动方程
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-07-04 DOI: 10.1134/S1234567825020053
Andrei Zotov
{"title":"On the Field Analogue of the Elliptic Spin Calogero–Moser Model: Lax Pair and Equations of Motion","authors":"Andrei Zotov","doi":"10.1134/S1234567825020053","DOIUrl":"10.1134/S1234567825020053","url":null,"abstract":"<p> A Lax pair for the field analogue of the classical spin elliptic Calogero–Moser model is proposed. Namely, using the previously known Lax matrix, we suggest an ansatz for the accompanying matrix. The presented construction is valid when the matrix of spin variables <span>({mathcal S}inoperatorname{Mat}(N,mathbb C))</span> satisfies the condition <span>({mathcal S}^2=c_0{mathcal S})</span> with some constant <span>(c_0inmathbb C)</span>. It is shown that the Lax pair satisfies the Zakharov–Shabat equation with unwanted term, thus providing equations of motion on the unreduced phase space. The unwanted term vanishes after additional reduction. In the special case <span>(operatorname{rank}(mathcal S)=1)</span>, we show that the reduction provides the Lax pair of the spinless field Calogero–Moser model obtained earlier by Akhmetshin, Krichever, and Volvovski. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 2","pages":"142 - 158"},"PeriodicalIF":0.7,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161914","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
Lagrangian Subvarieties of Hyperspherical Varieties Related to (G_2) 的超球变种的拉格朗日亚变种 (G_2)
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-07-04 DOI: 10.1134/S1234567825020089
Nikolay Kononenko
{"title":"Lagrangian Subvarieties of Hyperspherical Varieties Related to (G_2)","authors":"Nikolay Kononenko","doi":"10.1134/S1234567825020089","DOIUrl":"10.1134/S1234567825020089","url":null,"abstract":"<p> We consider two <span>(S)</span>-dual hyperspherical varieties of the group <span>(G_2timesoperatorname{SL}(2))</span>: an equivariant slice for <span>(G_2)</span> and the symplectic representation of <span>(G_2 times operatorname{SL}_2)</span> in the odd part of the basic classical Lie superalgebra <span>(mathfrak{g}(3))</span>. For these varieties, we check the equality of the numbers of irreducible components of their Lagrangian subvarieties (zero levels of the moment maps of Borel subgroups’ actions), conjectured by M. Finkelberg, V. Ginzburg, and R. Travkin. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 2","pages":"194 - 217"},"PeriodicalIF":0.7,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161507","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
Interpolation by Maximal Surfaces 最大曲面插值
IF 0.7 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-07-04 DOI: 10.1134/S1234567825020041
Rukmini Dey, Rahul Kumar Singh
{"title":"Interpolation by Maximal Surfaces","authors":"Rukmini Dey,&nbsp;Rahul Kumar Singh","doi":"10.1134/S1234567825020041","DOIUrl":"10.1134/S1234567825020041","url":null,"abstract":"<p> In this article, we use the inverse function theorem for Banach spaces to interpolate a given real analytic spacelike curve <span>(a)</span> in the Lorentz–Minkowski space <span>(mathbb{L}^3)</span> to another real analytic spacelike curve <span>(c)</span>, which is “close” enough to <span>(a)</span> in a certain sense, by constructing a maximal surface containing them. Throughout this study, the Björling problem and Schwarz’s solution to it play pivotal roles. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 2","pages":"126 - 141"},"PeriodicalIF":0.7,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161919","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 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
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