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Functional Analysis and Its Applications最新文献

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Pointwise Conditions for Membership of Functions in Weighted Sobolev Classes 加权Sobolev类中函数隶属性的点态条件
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2022-10-10 DOI: 10.1134/S0016266322020022
V. I. Bogachev
{"title":"Pointwise Conditions for Membership of Functions in Weighted Sobolev Classes","authors":"V. I. Bogachev","doi":"10.1134/S0016266322020022","DOIUrl":"10.1134/S0016266322020022","url":null,"abstract":"<p> According to a known characterization, a function <span>(f)</span> belongs to the Sobolev space <span>(W^{p,1}(mathbb{R}^n))</span> of functions contained in <span>(L^p(mathbb{R}^n))</span> along with their generalized first-order derivatives precisely when there is a function <span>(gin L^p(mathbb{R}^n))</span> such that </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 2","pages":"86 - 100"},"PeriodicalIF":0.4,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4741994","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
Estimation of the Modulus of Hölder Metric Regularity Hölder度量正则性模数的估计
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2022-10-10 DOI: 10.1134/S0016266322020071
Wending Xu
{"title":"Estimation of the Modulus of Hölder Metric Regularity","authors":"Wending Xu","doi":"10.1134/S0016266322020071","DOIUrl":"10.1134/S0016266322020071","url":null,"abstract":"<p> This paper mainly studies the modulus of Hölder metric regularity. The concepts of a generalized <span>(p)</span>-order Clarke-like set and generalized graphical derivative are introduced and used to estimate this modulus. The main result implies that it is bounded above by the upper limit of the inner norm of the inverse of generalized graphical derivative. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 2","pages":"138 - 143"},"PeriodicalIF":0.4,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4436501","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
Extension Operator for Subspaces of Vector Spaces over the Field (mathbb{F}_2) 域上向量空间子空间的可拓算子 (mathbb{F}_2)
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2022-10-10 DOI: 10.1134/S001626632202006X
O. V. Sipacheva, A. A. Solonkov
{"title":"Extension Operator for Subspaces of Vector Spaces over the Field (mathbb{F}_2)","authors":"O. V. Sipacheva,&nbsp;A. A. Solonkov","doi":"10.1134/S001626632202006X","DOIUrl":"10.1134/S001626632202006X","url":null,"abstract":"<p> In is proved that the free topological vector space <span>(B(X))</span> over the field <span>(mathbb{F}_2={0,1})</span> generated by a stratifiable space <span>(X)</span> is stratifiable, and therefore, for any closed subspace <span>(Fsubset B(X))</span> (in particular, for <span>(F=X)</span>) and any locally convex space <span>(E)</span>, there exists a linear extension operator <span>(C(F,E)to C(B(X),E))</span> between spaces of continuous maps. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 2","pages":"130 - 137"},"PeriodicalIF":0.4,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4438641","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)-Ergodicity of Convolution Operators in Group Algebras (A)群代数中卷积算子的遍历性
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2022-10-10 DOI: 10.1134/S0016266322020046
H. Mustafaev, A. Huseynli
{"title":"(A)-Ergodicity of Convolution Operators in Group Algebras","authors":"H. Mustafaev,&nbsp;A. Huseynli","doi":"10.1134/S0016266322020046","DOIUrl":"10.1134/S0016266322020046","url":null,"abstract":"<p> Let <span>(G)</span> be a locally compact Abelian group with dual group <span>(Gamma )</span>, let <span>(mu)</span> be a power bounded measure on <span>(G)</span>, and let <span>(A=[ a_{n,k}]_{n,k=0}^{infty})</span> be a strongly regular matrix. We show that the sequence <span>({sum_{k=0}^{infty}a_{n,k}mu^{k}ast f}_{n=0}^{infty})</span> converges in the <span>(L^{1})</span>-norm for every <span>(fin L^{1}(G))</span> if and only if <span>(mathcal{F}_{mu}:={gamma in Gamma:widehat{mu}(gamma) =1} )</span> is clopen in <span>(Gamma )</span>, where <span>(widehat{mu})</span> is the Fourier–Stieltjes transform of <span>(mu )</span>. If <span>(mu )</span> is a probability measure, then <span>(mathcal{F}_{mu})</span> is clopen in <span>(Gamma )</span> if and only if the closed subgroup generated by the support of <span>(mu )</span> is compact. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 2","pages":"110 - 115"},"PeriodicalIF":0.4,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4439301","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
Strengthening of the Bourgain–Kontorovich Theorem on Small Values of Hausdorff Dimension 关于Hausdorff维数小值的bourgin - kontorovich定理的强化
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2022-07-29 DOI: 10.1134/S0016266322010051
I. D. Kan
{"title":"Strengthening of the Bourgain–Kontorovich Theorem on Small Values of Hausdorff Dimension","authors":"I. D. Kan","doi":"10.1134/S0016266322010051","DOIUrl":"10.1134/S0016266322010051","url":null,"abstract":"<p> Let <span>(mathfrak{D}_mathbf{A}(N))</span> be the set of all integers not exceeding <span>(N)</span> and equal to irreducible denominators of positive rational numbers with finite continued fraction expansions in which all partial quotients belong to a finite number alphabet <span>(mathbf{A})</span>. A new lower bound for the cardinality <span>(|mathfrak{D}_mathbf{A}(N)|)</span> is obtained, whose nontrivial part improves that known previously by up to 28%. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 1","pages":"48 - 60"},"PeriodicalIF":0.4,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5117957","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: 3
On the Milnor and Tjurina Numbers of Zero-Dimensional Singularities 关于零维奇点的Milnor数和Tjurina数
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2022-07-29 DOI: 10.1134/S0016266322010014
A. G. Aleksandrov
{"title":"On the Milnor and Tjurina Numbers of Zero-Dimensional Singularities","authors":"A. G. Aleksandrov","doi":"10.1134/S0016266322010014","DOIUrl":"10.1134/S0016266322010014","url":null,"abstract":"<p> In this paper we study relationships between some topological and analytic invariants of zero-dimensional germs, or multiple points. Among other things, it is shown that there exist no rigid zero-dimensional Gorenstein singularities and rigid almost complete intersections. In the proof of the first result we exploit the canonical duality between homology and cohomology of the cotangent complex, while in the proof of the second we use a new method which is based on the properties of the torsion functor. In addition, we obtain highly efficient estimates for the dimension of the spaces of the first lower and upper cotangent functors of arbitrary zero-dimensional singularities, including the space of derivations. We also consider examples of nonsmoothable zero-dimensional noncomplete intersections and discuss some properties and methods for constructing such singularities using the theory of modular deformations, as well as a number of other applications. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 1","pages":"1 - 18"},"PeriodicalIF":0.4,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5121401","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
On a Notion of Averaged Mappings in (operatorname{CAT}(0)) Spaces 关于(operatorname{CAT}(0))空间中平均映射的一个概念
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2022-07-29 DOI: 10.1134/S0016266322010038
A. Bërdëllima
{"title":"On a Notion of Averaged Mappings in (operatorname{CAT}(0)) Spaces","authors":"A. Bërdëllima","doi":"10.1134/S0016266322010038","DOIUrl":"10.1134/S0016266322010038","url":null,"abstract":"<p> We introduce a notion of averaged mappings in the broader class of <span>(operatorname{CAT}(0))</span> spaces. We call these mappings <span>(alpha)</span>-firmly nonexpansive and develop basic calculus rules for ones that are quasi-<span>(alpha)</span>-firmly nonexpansive and have a common fixed point. We show that the iterates <span>(x_n:=Tx_{n-1})</span> of a nonexpansive mapping <span>(T)</span> converge weakly to an element in <span>(operatorname{Fix} T)</span> whenever <span>(T)</span> is quasi-<span>(alpha)</span>-firmly nonexpansive. Moreover, <span>(P_{operatorname{Fix} T}x_n)</span> converge strongly to this weak limit. Our theory is illustrated with two classical examples of cyclic and averaged projections. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 1","pages":"27 - 36"},"PeriodicalIF":0.4,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5121388","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
Two-Sided Estimates of the (K)-Functional for Spaces of Functions of Generalized Bounded Variation 广义有界变分函数空间(K)泛函的双面估计
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2022-07-29 DOI: 10.1134/S0016266322010026
E. I. Berezhnoi
{"title":"Two-Sided Estimates of the (K)-Functional for Spaces of Functions of Generalized Bounded Variation","authors":"E. I. Berezhnoi","doi":"10.1134/S0016266322010026","DOIUrl":"10.1134/S0016266322010026","url":null,"abstract":"<p> A two-sided estimate is proposed for the <span>(K)</span>-functional of the pair <span>((C[0,1], BV(X)))</span>, where <span>(BV(X))</span> is the space of functions of generalized bounded variation constructed from a symmetric sequence space <span>(X)</span>. The application of this estimate to various sequence spaces <span>(X)</span> yields new interpolation theorems for spaces of finite Wiener–Young <span>(h)</span>-variation, of finite Waterman <span>(Lambda)</span>-variation, of bounded modulus of variation in the sense of Chanturiya, etc. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 1","pages":"19 - 26"},"PeriodicalIF":0.4,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5121405","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
Polynomials in the Differentiation Operator and Formulas for the Sums of Certain Convergent Series 微分算子中的多项式及收敛级数和的公式
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2022-07-29 DOI: 10.1134/S0016266322010063
K. A. Mirzoev, T. A. Safonova
{"title":"Polynomials in the Differentiation Operator and Formulas for the Sums of Certain Convergent Series","authors":"K. A. Mirzoev,&nbsp;T. A. Safonova","doi":"10.1134/S0016266322010063","DOIUrl":"10.1134/S0016266322010063","url":null,"abstract":"<p> Let <span>(P_n(x))</span> be any polynomial of degree <span>(ngeq 2)</span> with real coefficients such that <span>(P_n(k)ne 0)</span> for <span>(kinmathbb{Z})</span>. In the paper, in particular, the sum of a series of the form <span>(sum_{k=-infty}^{+infty}1/P_n(k))</span> is expressed as the value at <span>((0,0))</span> of the Green function of the self-adjoint problem generated by the differential expression <span>(l_n[y]=P_n(i,d/dx) y)</span> and the boundary conditions <span>(y^{(j)}(0)=y^{(j)}(2pi))</span> (<span>(j=0,1,dots,n-1)</span>). Thus, such a sum is explicitly expressed in terms of the value of an easy-to-construct elementary function. These formulas, obviously, also apply to sums of the form <span>(sum_{k=0}^{+infty}1/P_n(k^2))</span>, while it is well known that similar general formulas for the sum <span>(sum_{k=0}^{+infty}1/P_n(k))</span> do not exist. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 1","pages":"61 - 71"},"PeriodicalIF":0.4,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5117958","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
Wold-Type Decompositions for Pairs of Commutative Semigroups Generated by Isometries 等距生成的交换半群对的世界型分解
IF 0.4 4区 数学
Functional Analysis and Its Applications Pub Date : 2022-07-29 DOI: 10.1134/S001626632201004X
T. Bînzar, C. Lăzureanu
{"title":"Wold-Type Decompositions for Pairs of Commutative Semigroups Generated by Isometries","authors":"T. Bînzar,&nbsp;C. Lăzureanu","doi":"10.1134/S001626632201004X","DOIUrl":"10.1134/S001626632201004X","url":null,"abstract":"<p> In this paper we analyze connections between Wold-type decompositions of bi/isometries and pairs of semigroups of isometries, where at least one of semigroups is a product semigroup generated by two isometries. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"56 1","pages":"37 - 47"},"PeriodicalIF":0.4,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5121406","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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