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Functional Analysis and Its Applications最新文献

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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":"56 4","pages":"269 - 281"},"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":"56 3","pages":"199 - 215"},"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":"56 3","pages":"216 - 224"},"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":"56 3","pages":"188 - 198"},"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
On Poisson Semigroup Hypercontractivity for Higher-Dimensional Spheres 高维球的泊松半群超收缩性
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-01-31 DOI: 10.1134/S001626632203008X
Yi. C. Huang
{"title":"On Poisson Semigroup Hypercontractivity for Higher-Dimensional Spheres","authors":"Yi. C. Huang","doi":"10.1134/S001626632203008X","DOIUrl":"10.1134/S001626632203008X","url":null,"abstract":"<p> In this note we consider a variant of a question of Mueller and Weissler raised in 1982, thereby complementing a classical result of Beckner on Stein’s conjecture and a recent result of Frank and Ivanisvili. More precisely, we show that, for <span>(1&lt;pleq q&lt;infty)</span> and <span>(ngeq1)</span>, the Poisson semigroup <span>(e^{-tsqrt{-Delta-(n-1)mathbb{P}}})</span> on the <span>(n)</span>-sphere is hypercontractive from <span>(L^p)</span> to <span>(L^q)</span> if and only if <span>(e^{-t}leqsqrt{(p-1)/(q-1)})</span>; here <span>(Delta)</span> is the Laplace–Beltrami operator on the <span>(n)</span>-sphere and <span>(mathbb{P})</span> is the projection operator onto spherical harmonics of degree <span>(geq1)</span>. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 3","pages":"235 - 238"},"PeriodicalIF":0.4,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5175322","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
Parametric Korteweg–de Vries Hierarchy and Hyperelliptic Sigma Functions 参数Korteweg-de Vries层次和超椭圆Sigma函数
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-01-31 DOI: 10.1134/S0016266322030029
E. Yu. Bunkova, V. M. Bukhshtaber
{"title":"Parametric Korteweg–de Vries Hierarchy and Hyperelliptic Sigma Functions","authors":"E. Yu. Bunkova,&nbsp;V. M. Bukhshtaber","doi":"10.1134/S0016266322030029","DOIUrl":"10.1134/S0016266322030029","url":null,"abstract":"<p> In this paper, a parametric Korteweg–de Vries hierarchy is defined that depends on an infinite set of graded parameters <span>(a = (a_4,a_6,dots))</span>. It is shown that, for any genus <span>(g)</span>, the Klein hyperelliptic function <span>(wp_{1,1}(t,lambda))</span> defined on the basis of the multidimensional sigma function <span>(sigma(t, lambda))</span>, where <span>(t = (t_1, t_3,dots, t_{2g-1}))</span> and <span>(lambda = (lambda_4, lambda_6,dots, lambda_{4 g + 2}))</span>, specifies a solution to this hierarchy in which the parameters <span>(a)</span> are given as polynomials in the parameters <span>(lambda)</span> of the sigma function. The proof uses results concerning the family of operators introduced by V. M. Buchstaber and S. Yu. Shorina. This family consists of <span>(g)</span> third-order differential operators in <span>(g)</span> variables. Such families are defined for all <span>(g geqslant 1)</span>, the operators in each of them pairwise commute with each other and also commute with the Schrödinger operator. In this paper a relationship between these families and the Korteweg–de Vries parametric hierarchy is described. A similar infinite family of third-order operators on an infinite set of variables is constructed. The results obtained are extended to the case of such a family. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 3","pages":"169 - 187"},"PeriodicalIF":0.4,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5175319","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
Absolute Continuity and Singularity of Spectra for the Flows (T_totimes T_{at}) 流动光谱的绝对连续性和奇异性 (T_totimes T_{at})
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-01-31 DOI: 10.1134/S0016266322030066
V. V. Ryzhikov
{"title":"Absolute Continuity and Singularity of Spectra for the Flows (T_totimes T_{at})","authors":"V. V. Ryzhikov","doi":"10.1134/S0016266322030066","DOIUrl":"10.1134/S0016266322030066","url":null,"abstract":"<p> Given disjoint countable dense subsets <span>(C)</span> and <span>(D)</span> of the half-line <span>((1,+infty))</span>, there exists a flow <span>(T_t)</span> preserving a sigma-finite measure and such that all automorphisms <span>(T_1otimes T_{c})</span> with <span>(cin C)</span> have simple singular spectrum and all automorphisms <span>(T_1otimes T_{d})</span> with <span>(din D)</span> have Lebesgue spectrum of countable multiplicity. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 3","pages":"225 - 228"},"PeriodicalIF":0.4,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5176485","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
Homogenization of the Schrödinger-Type Equations: Operator Estimates with Correctors Schrödinger-Type方程的均匀化:带校正器的算子估计
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-01-31 DOI: 10.1134/S0016266322030078
T. A. Suslina
{"title":"Homogenization of the Schrödinger-Type Equations: Operator Estimates with Correctors","authors":"T. A. Suslina","doi":"10.1134/S0016266322030078","DOIUrl":"10.1134/S0016266322030078","url":null,"abstract":"<p> In <span>(L_2(mathbb R^d;mathbb C^n))</span> we consider a self-adjoint elliptic second-order differential operator <span>(A_varepsilon)</span>. It is assumed that the coefficients of <span>(A_varepsilon)</span> are periodic and depend on <span>(mathbf x/varepsilon)</span>, where <span>(varepsilon&gt;0)</span> is a small parameter. We study the behavior of the operator exponential <span>(e^{-iA_varepsilontau})</span> for small <span>(varepsilon)</span> and <span>(tauinmathbb R)</span>. The results are applied to study the behavior of the solution of the Cauchy problem for the Schrödinger-type equation <span>(ipartial_tau mathbf{u}_varepsilon(mathbf x,tau) = - (A_varepsilon{mathbf u}_varepsilon)(mathbf x,tau))</span> with initial data in a special class. For fixed <span>(tau)</span> and <span>(varepsilonto 0)</span>, the solution <span>({mathbf u}_varepsilon(,boldsymbolcdot,,tau))</span> converges in <span>(L_2(mathbb R^d;mathbb C^n))</span> to the solution of the homogenized problem; the error is of order <span>(O(varepsilon))</span>. We obtain approximations for the solution <span>({mathbf u}_varepsilon(,boldsymbolcdot,,tau))</span> in <span>(L_2(mathbb R^d;mathbb C^n))</span> with error <span>(O(varepsilon^2))</span> and in <span>(H^1(mathbb R^d;mathbb C^n))</span> with error <span>(O(varepsilon))</span>. These approximations involve appropriate correctors. The dependence of errors on <span>(tau)</span> is traced. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 3","pages":"229 - 234"},"PeriodicalIF":0.4,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5179229","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
Taylor Spectrum for Modules over Lie Algebras 李代数上模的泰勒谱
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2023-01-31 DOI: 10.1134/S0016266322030017
B. I. Bilich
{"title":"Taylor Spectrum for Modules over Lie Algebras","authors":"B. I. Bilich","doi":"10.1134/S0016266322030017","DOIUrl":"10.1134/S0016266322030017","url":null,"abstract":"<p> In this paper we generalize the notion of the Taylor spectrum to modules over an arbitrary Lie algebra and study it for finite-dimensional modules. We show that the spectrum can be described as the set of simple submodules in the case of nilpotent and semisimple Lie algebras. We also show that this result does not hold for solvable Lie algebras and obtain a precise description of the spectrum in the case of Borel subalgebras of semisimple Lie algebras. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 3","pages":"159 - 168"},"PeriodicalIF":0.4,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5173370","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
Approximation of Operator Semigroups Using Linear-Fractional Operator Functions and Weighted Averages 利用线性分数阶算子函数和加权平均逼近算子半群
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2022-10-10 DOI: 10.1134/S0016266322020058
J. L. Rogava
{"title":"Approximation of Operator Semigroups Using Linear-Fractional Operator Functions and Weighted Averages","authors":"J. L. Rogava","doi":"10.1134/S0016266322020058","DOIUrl":"10.1134/S0016266322020058","url":null,"abstract":"<p> An analytic semigroup of operators on a Banach space is approximated by a sequence of positive integer powers of a linear-fractional operator function. It is proved that the order of the approximation error in the domain of the generating operator equals <span>(O(n^{-2}ln(n)))</span>. For a self-adjoint positive definite operator <span>(A)</span> decomposed into a sum of self-adjoint positive definite operators, an approximation of the semigroup <span>(exp(-tA))</span> (<span>(tgeq0)</span>) by weighted averages is also considered. It is proved that the order of the approximation error in the operator norm equals <span>(O(n^{-1/2}ln(n)))</span>. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 2","pages":"116 - 129"},"PeriodicalIF":0.4,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4436500","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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