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Functional Analysis and Its Applications最新文献

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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":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":"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":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":"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":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":"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":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":"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":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":"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":null,"pages":null},"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
On the Arens Homomorphism 关于阿伦斯同态
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2022-10-10 DOI: 10.1134/S0016266322020083
B. Turan, M. Aslantaş
{"title":"On the Arens Homomorphism","authors":"B. Turan,&nbsp;M. Aslantaş","doi":"10.1134/S0016266322020083","DOIUrl":"10.1134/S0016266322020083","url":null,"abstract":"<p> Let <span>(E)</span> be a unital <span>(f)</span>-module over an <span>(f)</span>-algebra <span>(A)</span>. With the help of Arens extension theory, a <span>((A^{sim})_{n}^{sim})</span> module structure on <span>(E^{sim})</span> can be defined. The paper deals mainly with properties of the Arens homomorphism <span>(etacolon(A^{sim})_{n}^{sim}to operatorname {Orth}(E^{sim}))</span>, which is defined by the <span>((A^{sim})_{n}^{sim})</span> module structure on <span>(E^{sim})</span>. Necessary and sufficient conditions for an <span>(A)</span> submodule of <span>(E)</span> to be an order ideal are obtained. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4438623","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
Newton Polytopes of Nondegenerate Quadratic Forms 非退化二次型的牛顿多面体
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2022-10-10 DOI: 10.1134/S0016266322020095
A. Yu. Yuran
{"title":"Newton Polytopes of Nondegenerate Quadratic Forms","authors":"A. Yu. Yuran","doi":"10.1134/S0016266322020095","DOIUrl":"10.1134/S0016266322020095","url":null,"abstract":"<p> We characterize Newton polytopes of nondegenerate quadratic forms and Newton polyhedra of Morse singularities. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4439302","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
Extended Spectra for Some Composition Operators on Weighted Hardy Spaces 加权Hardy空间上一些复合算子的扩展谱
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2022-10-10 DOI: 10.1134/S0016266322020010
I. F. Z. Bensaid, F. León-Saavedra, P. Romero de la Rosa
{"title":"Extended Spectra for Some Composition Operators on Weighted Hardy Spaces","authors":"I. F. Z. Bensaid,&nbsp;F. León-Saavedra,&nbsp;P. Romero de la Rosa","doi":"10.1134/S0016266322020010","DOIUrl":"10.1134/S0016266322020010","url":null,"abstract":"<p> Let <span>(alpha)</span> be a complex scalar, and let <span>(A)</span> be a bounded linear operator on a Hilbert space <span>(H)</span>. We say that <span>(alpha)</span> is an extended eigenvalue of <span>(A)</span> if there exists a nonzero bounded linear operator <span>(X)</span> such that <span>(AX=alpha XA)</span>. In weighted Hardy spaces invariant under automorphisms, we completely compute the extended eigenvalues of composition operators induced by linear fractional self-mappings of the unit disk <span>(mathbb{D})</span> with one fixed point in <span>(mathbb{D})</span> and one outside <span>(overline{mathbb{D}})</span>. Such classes of transformations include elliptic and loxodromic mappings as well as a hyperbolic nonautomorphic mapping. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4436495","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
Distributions of Polynomials in Gaussian Random Variables under Constraints on the Powers of Variables 变量幂约束下高斯随机变量中多项式的分布
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2022-10-10 DOI: 10.1134/S0016266322020034
E. D. Kosov
{"title":"Distributions of Polynomials in Gaussian Random Variables under Constraints on the Powers of Variables","authors":"E. D. Kosov","doi":"10.1134/S0016266322020034","DOIUrl":"10.1134/S0016266322020034","url":null,"abstract":"<p> We study the densities of measures that are polynomial images of the standard Gaussian measure on <span>(mathbb{R}^n)</span>. We assume that the degree of a polynomial is fixed and each variable appears in the monomials of the polynomial to powers bounded by another fixed number. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4438649","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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