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Functional Analysis and Its Applications最新文献

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On Bloch Solutions of Difference Schrödinger Equations 差分Schrödinger方程的Bloch解
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-04-13 DOI: 10.1134/S0016266322040013
D. I. Borisov, A. A. Fedotov
{"title":"On Bloch Solutions of Difference Schrödinger Equations","authors":"D. I. Borisov,&nbsp;A. A. Fedotov","doi":"10.1134/S0016266322040013","DOIUrl":"10.1134/S0016266322040013","url":null,"abstract":"<p> Bloch solutions of the difference Schrödinger equation with periodic complex potential on the real line are discussed. The case where the spectral parameter is outside the spectrum of the corresponding Schrödinger operator is considered. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 4","pages":"239 - 250"},"PeriodicalIF":0.4,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4525197","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: 1
Hermitian Property and the Simplicity of Spectrum of Bethe Subalgebras in Yangians yangian中Bethe子代数的厄米性质和谱的简单性
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-04-13 DOI: 10.1134/S0016266322040098
I. A. Mashanova-Golikova
{"title":"Hermitian Property and the Simplicity of Spectrum of Bethe Subalgebras in Yangians","authors":"I. A. Mashanova-Golikova","doi":"10.1134/S0016266322040098","DOIUrl":"10.1134/S0016266322040098","url":null,"abstract":"<p> The image of the Bethe subalgebra <span>(B(C))</span> in the tensor product of representations of the Yangian <span>(Y(mathfrak{gl}_n))</span> contains the full set of Hamiltonians of the Heisenberg magnet chain XXX. The main problem in the XXX integrable system is the diagonalization of the operators by which the elements of Bethe subalgebras act on the corresponding representations of the Yangian. The standard approach is the Bethe ansatz. As the first step toward solving this problem, we want to show that the eigenvalues of these operators have multiplicity 1. In this work we obtained several new results on the simplicity of spectra of Bethe subalgebras in Kirillov–Reshetikhin modules in the case of <span>(Y(mathfrak{g}))</span>, where <span>(mathfrak{g})</span> is a simple Lie algebra. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 4","pages":"320 - 323"},"PeriodicalIF":0.4,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4519465","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
One-Dimensional Central Measures on Numberings of Ordered Sets 有序集编号的一维中心测度
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-04-13 DOI: 10.1134/S0016266322040025
A. M. Vershik
{"title":"One-Dimensional Central Measures on Numberings of Ordered Sets","authors":"A. M. Vershik","doi":"10.1134/S0016266322040025","DOIUrl":"10.1134/S0016266322040025","url":null,"abstract":"<p> We describe one-dimensional central measures on numberings (tableaux) of ideals of partially ordered sets (posets). As the main example, we study the poset <span>(mathbb{Z}_+^d)</span> and the graph of its finite ideals, multidimensional Young tableaux; for <span>(d=2)</span>, this is the ordinary Young graph. The central measures are stratified by dimension; in the paper we give a complete description of the one-dimensional stratum and prove that every ergodic central measure is uniquely determined by its frequencies. The suggested method, in particular, gives the first purely combinatorial proof of E. Thoma’s theorem for one-dimensional central measures different from the Plancherel measure (which is of dimension <span>(2)</span>). </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 4","pages":"251 - 256"},"PeriodicalIF":0.4,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4521274","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 Extension of Functions from Countable Subspaces 论可数子空间中函数的可拓性
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-04-13 DOI: 10.1134/S0016266322040049
A. Yu. Groznova
{"title":"On the Extension of Functions from Countable Subspaces","authors":"A. Yu. Groznova","doi":"10.1134/S0016266322040049","DOIUrl":"10.1134/S0016266322040049","url":null,"abstract":"<p> Three intermediate class of spaces <span>(mathscr{R}_1subset mathscr{R}_2subset mathscr{R}_3)</span> between the classes of <span>(F)</span>- and <span>(betaomega)</span>-spaces are considered. The <span>(mathscr{R}_1)</span>- and <span>(mathscr{R}_3)</span>-spaces are characterized in terms of the extension of functions. It is proved that the classes of <span>(mathscr{R}_1)</span>-, <span>(mathscr{R}_2)</span>-, <span>(mathscr{R}_3)</span>-, and <span>(betaomega)</span>-spaces are not preserved by the Stone–Čech compactification. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 4","pages":"264 - 268"},"PeriodicalIF":0.4,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4524184","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
Restricted Partitions: The Polynomial Case 限制分区:多项式情况
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-04-13 DOI: 10.1134/S0016266322040074
V. L. Chernyshev, T. W. Hilberdink, D. S. Minenkov, V. E. Nazaikinskii
{"title":"Restricted Partitions: The Polynomial Case","authors":"V. L. Chernyshev,&nbsp;T. W. Hilberdink,&nbsp;D. S. Minenkov,&nbsp;V. E. Nazaikinskii","doi":"10.1134/S0016266322040074","DOIUrl":"10.1134/S0016266322040074","url":null,"abstract":"<p> We prove a restricted inverse prime number theorem for an arithmetical semigroup with polynomial growth of the abstract prime counting function. The adjective “restricted” refers to the fact that we consider the counting function of abstract integers of degree <span>(le t)</span> whose prime factorization may only contain the first <span>(k)</span> abstract primes (arranged in nondescending order of their degree). The theorem provides the asymptotics of this counting function as <span>(t,ktoinfty)</span>. The study of the discussed asymptotics is motivated by two possible applications in mathematical physics: the calculation of the entropy of generalizations of the Bose gas and the study of the statistics of propagation of narrow wave packets on metric graphs. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 4","pages":"299 - 309"},"PeriodicalIF":0.4,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4817408","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
Superposition Principle for the Fokker–Planck–Kolmogorov Equations with Unbounded Coefficients 系数无界的Fokker-Planck-Kolmogorov方程的叠加原理
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-04-13 DOI: 10.1134/S0016266322040062
T. I. Krasovitskii, S. V. Shaposhnikov
{"title":"Superposition Principle for the Fokker–Planck–Kolmogorov Equations with Unbounded Coefficients","authors":"T. I. Krasovitskii,&nbsp;S. V. Shaposhnikov","doi":"10.1134/S0016266322040062","DOIUrl":"10.1134/S0016266322040062","url":null,"abstract":"<p> The superposition principle delivers a probabilistic representation of a solution <span>({mu_t}_{tin[0, T]})</span> of the Fokker–Planck–Kolmogorov equation <span>(partial_tmu_t=L^{*}mu_t)</span> in terms of a solution <span>(P)</span> of the martingale problem with operator <span>(L)</span>. We generalize the superposition principle to the case of equations on a domain, examine the transformation of the measure <span>(P)</span> and the operator <span>(L)</span> under a change of variables, and obtain new conditions for the validity of the superposition principle under the assumption of the existence of a Lyapunov function for the unbounded part of the drift coefficient. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 4","pages":"282 - 298"},"PeriodicalIF":0.4,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4519435","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
Improved Resolvent Approximations in Homogenization of Second-Order Operators with Periodic Coefficients 二阶周期系数算子齐次化的改进求解逼近
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-04-13 DOI: 10.1134/S0016266322040086
S. E. Pastukhova
{"title":"Improved Resolvent Approximations in Homogenization of Second-Order Operators with Periodic Coefficients","authors":"S. E. Pastukhova","doi":"10.1134/S0016266322040086","DOIUrl":"10.1134/S0016266322040086","url":null,"abstract":"<p> For elliptic divergent self-adjoint second-order operators with <span>(varepsilon)</span>-periodic measurable coefficients acting on the whole space <span>(mathbb{R}^d)</span>, resolvent approximations in the operator norm <span>(|!,boldsymbolcdot,!|_{H^1to H^1})</span> with remainder of order <span>(varepsilon^2)</span> as <span>(varepsilonto 0)</span> are found by the method of two-scale expansions with the use of smoothing. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 4","pages":"310 - 319"},"PeriodicalIF":0.4,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4525641","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 Maximal Extensions of Nilpotent Lie Algebras 幂零李代数的极大扩展
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-04-13 DOI: 10.1134/S0016266322040037
V. V. Gorbatsevich
{"title":"On Maximal Extensions of Nilpotent Lie Algebras","authors":"V. V. Gorbatsevich","doi":"10.1134/S0016266322040037","DOIUrl":"10.1134/S0016266322040037","url":null,"abstract":"<p> Extensions of finite-dimensional nilpotent Lie algebras, in particular, solvable extensions, are considered. Some properties of maximal extensions are proved. A counterexample to L. Šnobl’s conjecture concerning the uniqueness of maximal solvable extensions is constructed. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 4","pages":"257 - 263"},"PeriodicalIF":0.4,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4524534","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
Unitary Flows with Tensor Simple Spectrum 具有张量简单谱的酉流
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-04-13 DOI: 10.1134/S0016266322040116
V. V. Ryzhikov
{"title":"Unitary Flows with Tensor Simple Spectrum","authors":"V. V. Ryzhikov","doi":"10.1134/S0016266322040116","DOIUrl":"10.1134/S0016266322040116","url":null,"abstract":"<p> Unitary flows <span>(T_t)</span> of dynamical origin such that, for any countable <span>(Qsubset (0,+infty))</span>, the spectrum of the tensor product <span>(bigotimes_{qin Q} T_q )</span> is simple are constructed. All typical flows preserving a sigma-finite measure have this property. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 4","pages":"327 - 330"},"PeriodicalIF":0.4,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4521281","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 an Elliptic Operator Degenerating on the Boundary 关于椭圆算子在边界上的退化
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-04-13 DOI: 10.1134/S0016266322040104
V. E. Nazaikinskii
{"title":"On an Elliptic Operator Degenerating on the Boundary","authors":"V. E. Nazaikinskii","doi":"10.1134/S0016266322040104","DOIUrl":"10.1134/S0016266322040104","url":null,"abstract":"<p> Let <span>(Omegasubsetmathbb{R}^n)</span> be a bounded domain with smooth boundary <span>(partialOmega)</span>, let <span>(D(x)in C^infty(overlineOmega))</span> be a defining function of the boundary, and let <span>(B(x)in C^infty(overlineOmega))</span> be an <span>(ntimes n)</span> matrix function with self-adjoint positive definite values <span>(B(x )=B^*(x)&gt;0)</span> for all <span>(xinoverlineOmega)</span> The Friedrichs extension of the minimal operator given by the differential expression <span>(mathcal{A}_0=-langlenabla,D(x )B(x)nablarangle)</span> to <span>(C_0^infty(Omega))</span> is described. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 4","pages":"324 - 326"},"PeriodicalIF":0.4,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4524194","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: 1
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