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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
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
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
Complement Property and Frames in the Phase Retrieval Problem 相位检索问题中的补码属性和帧
IF 0.6 4区 数学
Functional Analysis and Its Applications Pub Date : 2025-04-16 DOI: 10.1134/S1234567825010021
Ilya Izbiakov, Sergey Novikov, Pavel Terekhin
{"title":"Complement Property and Frames in the Phase Retrieval Problem","authors":"Ilya Izbiakov,&nbsp;Sergey Novikov,&nbsp;Pavel Terekhin","doi":"10.1134/S1234567825010021","DOIUrl":"10.1134/S1234567825010021","url":null,"abstract":"<p> Sequences of elements from a Hilbert space with phase retrieval property are considered. We discuss a connection between the phase retrieval property, the complement property, and the full spark property (strongly complete systems). There are conditions on the reproducing kernels in the Hardy space of holomorphic functions which ensure phase recovery. We use not only Hilbert, but also Banach frames to construct such sequences of reproducing kernels. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"59 1","pages":"11 - 18"},"PeriodicalIF":0.6,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143840433","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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