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Functional Analysis and Its Applications最新文献

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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":null,"pages":null},"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":null,"pages":null},"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
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":null,"pages":null},"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
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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
Approximations of the Images and Integral Funnels of the (L_p) Balls under a Urysohn-Type Integral Operator urysohn型积分算子下(L_p)球的像和积分漏斗的逼近
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-04-13 DOI: 10.1134/S0016266322040050
A. Huseyin, N. Huseyin, Kh. G. Guseinov
{"title":"Approximations of the Images and Integral Funnels of the (L_p) Balls under a Urysohn-Type Integral Operator","authors":"A. Huseyin,&nbsp;N. Huseyin,&nbsp;Kh. G. Guseinov","doi":"10.1134/S0016266322040050","DOIUrl":"10.1134/S0016266322040050","url":null,"abstract":"<p> Approximations of the image and integral funnel of a closed ball of the space <span>(L_p)</span>, <span>(p&gt;1)</span>, under a Urysohn-type integral operator are considered. A closed ball of the space <span>(L_p)</span>, <span>(p&gt;1)</span>, is replaced by a set consisting of a finite number of piecewise constant functions, and it is proved that, for appropriate discretization parameters, the images of these piecewise constant functions form an internal approximation of the image of the closed ball. This result is applied to approximate the integral funnel of a closed ball of the space <span>(L_p)</span>, <span>(p&gt;1)</span>, under a Urysohn-type integral operator by a set consisting of a finite number of points. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4524185","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
Semifinite Harmonic Functions on the Zigzag Graph z形图上的半有限调和函数
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-01-31 DOI: 10.1134/S0016266322030042
N. A. Safonkin
{"title":"Semifinite Harmonic Functions on the Zigzag Graph","authors":"N. A. Safonkin","doi":"10.1134/S0016266322030042","DOIUrl":"10.1134/S0016266322030042","url":null,"abstract":"<p> We study semifinite harmonic functions on the zigzag graph, which corresponds to the Pieri rule for the fundamental quasisymmetric functions <span>({F_{lambda}})</span>. The main problem, which we solve here, is to classify the indecomposable semifinite harmonic functions on this graph. We show that these functions are in a natural bijective correspondence with some combinatorial data, the so-called semifinite zigzag growth models. Furthermore, we describe an explicit construction that produces a semifinite indecomposable harmonic function from every semifinite zigzag growth model. We also establish a semifinite analogue of the Vershik–Kerov ring theorem. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5175321","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: 2
Criteria for the Property (UWE) and the a-Weyl Theorem 性质判据(UWE)和a-Weyl定理
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-01-31 DOI: 10.1134/S0016266322030054
Chenhui Sun, Xiaohong Cao
{"title":"Criteria for the Property (UWE) and the a-Weyl Theorem","authors":"Chenhui Sun,&nbsp;Xiaohong Cao","doi":"10.1134/S0016266322030054","DOIUrl":"10.1134/S0016266322030054","url":null,"abstract":"<p> In this paper, the property (UWE) and the a-Weyl theorem for bounded linear operators are studied in terms of the property of topological uniform descent. Sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space to have the property (UWE) and satisfy the a-Weyl theorem are established. In addition, new criteria for the fulfillment of the property (UWE) and the a-Weyl theorem for an operator function are discussed. As a consequence of the main theorem, results on the stability of the property (UWE) and the a-Weyl theorem are obtained. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5172988","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
Cyclic Vectors and Invariant Subspaces of the Backward Shift Operator in Schwartz Modules Schwartz模中倒移算子的循环向量和不变子空间
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-01-31 DOI: 10.1134/S0016266322030030
O. A. Ivanova, S. N. Melikhov
{"title":"Cyclic Vectors and Invariant Subspaces of the Backward Shift Operator in Schwartz Modules","authors":"O. A. Ivanova,&nbsp;S. N. Melikhov","doi":"10.1134/S0016266322030030","DOIUrl":"10.1134/S0016266322030030","url":null,"abstract":"<p> Cyclic vectors and proper closed invariant subspaces of the backward shift operator in the Schwartz modules of entire functions of exponential type are described. The results are applied to describe ideals of the algebra of infinitely differentiable functions on a closed or open interval containing <span>(0)</span> with Duhamel product as multiplication. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5175320","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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