Pub Date : 2023-12-29DOI: 10.1134/S0016266323020016
E. I. Berezhnoi
On the basis of a new approach to the Calderón construction (X_0^{theta} X_1^{1-theta}) for ideal spaces (X_0) and (X_1) and a parameter (theta in [0,1]), final results concerning a description of multipliers spaces are obtained. In particular, it is shown that if ideal spaces (X_0) and (X_1) have the Fatou property, then (M(X_0^{theta_0} X_1^{1-theta_0},{to},X_0^{theta_1} X_1^{1-theta_1}) = M(X_1^{theta_1 - theta_0} to X_0^{theta_1 -theta_0})) for (0 <theta_0 <theta_1 <1). Due to the absence of constraints on the ideal spaces (X_0) and (X_1), the obtained results apply to a large class of ideal spaces.
{"title":"Multipliers for the Calderón Construction","authors":"E. I. Berezhnoi","doi":"10.1134/S0016266323020016","DOIUrl":"10.1134/S0016266323020016","url":null,"abstract":"<p> On the basis of a new approach to the Calderón construction <span>(X_0^{theta} X_1^{1-theta})</span> for ideal spaces <span>(X_0)</span> and <span>(X_1)</span> and a parameter <span>(theta in [0,1])</span>, final results concerning a description of multipliers spaces are obtained. In particular, it is shown that if ideal spaces <span>(X_0)</span> and <span>(X_1)</span> have the Fatou property, then <span>(M(X_0^{theta_0} X_1^{1-theta_0},{to},X_0^{theta_1} X_1^{1-theta_1}) = M(X_1^{theta_1 - theta_0} to X_0^{theta_1 -theta_0}))</span> for <span>(0 <theta_0 <theta_1 <1)</span>. Due to the absence of constraints on the ideal spaces <span>(X_0)</span> and <span>(X_1)</span>, the obtained results apply to a large class of ideal spaces. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 2","pages":"87 - 98"},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139069592","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}
Pub Date : 2023-12-29DOI: 10.1134/S001626632302003X
Zhijie Dong, Haitao Ma
We define certain subvarieties, called (theta)-Hecke correspondences, in Cartesian products of diagram automorphism fixed quiver varieties. These give us generators of diagram automorphism fixed Lie algebras.
Abstract We define certain subvarieties, called (theta)-Hecke correspondences, in Cartesian product of diagram automorphism fixed quiver varieties.这些子域给我们提供了图自动态固定李代数的生成器。
{"title":"Diagram Automorphism Fixed Lie Algebras and Diagram Automorphism Fixed Quiver Varieties","authors":"Zhijie Dong, Haitao Ma","doi":"10.1134/S001626632302003X","DOIUrl":"10.1134/S001626632302003X","url":null,"abstract":"<p> We define certain subvarieties, called <span>(theta)</span>-Hecke correspondences, in Cartesian products of diagram automorphism fixed quiver varieties. These give us generators of diagram automorphism fixed Lie algebras. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 2","pages":"109 - 116"},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139069471","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}
Pub Date : 2023-12-29DOI: 10.1134/S0016266323020053
S. A. Stepin
The spectral properties of the generator of an evolution semigroup describing the dynamics of particle transport in a substance are studied. An effective estimate of the number of unstable modes is obtained, and geometric conditions for spectral stability and instability are found.
{"title":"Spectral Analysis of a Dynamical System Describing the Diffusion of Neutrons","authors":"S. A. Stepin","doi":"10.1134/S0016266323020053","DOIUrl":"10.1134/S0016266323020053","url":null,"abstract":"<p> The spectral properties of the generator of an evolution semigroup describing the dynamics of particle transport in a substance are studied. An effective estimate of the number of unstable modes is obtained, and geometric conditions for spectral stability and instability are found. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 2","pages":"143 - 157"},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139069401","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}
Pub Date : 2023-09-05DOI: 10.1134/S0016266323010045
D. V. Zanin, F. A. Sukochev
A version of Connes Integration Formula which provides concrete asymptotics of eigenvalues is given. This radically extends the class of quantum-integrable functions on compact Riemannian manifolds.
{"title":"Connes Integration Formula: A Constructive Approach","authors":"D. V. Zanin, F. A. Sukochev","doi":"10.1134/S0016266323010045","DOIUrl":"10.1134/S0016266323010045","url":null,"abstract":"<p> A version of Connes Integration Formula which provides concrete asymptotics of eigenvalues is given. This radically extends the class of quantum-integrable functions on compact Riemannian manifolds. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 1","pages":"40 - 59"},"PeriodicalIF":0.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4231634","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}
Pub Date : 2023-09-05DOI: 10.1134/S0016266323010094
V. D. Sedykh
It is proved that the image of a stable germ of type (E_6^pm) of a Lagrangian map to (mathbb R^n) is homeomorphic to the germ at zero of a closed half-space.
{"title":"The Image of a Lagrangian Germ of Type (E_6^pm)","authors":"V. D. Sedykh","doi":"10.1134/S0016266323010094","DOIUrl":"10.1134/S0016266323010094","url":null,"abstract":"<p> It is proved that the image of a stable germ of type <span>(E_6^pm)</span> of a Lagrangian map to <span>(mathbb R^n)</span> is homeomorphic to the germ at zero of a closed half-space. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 1","pages":"80 - 82"},"PeriodicalIF":0.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4233945","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}
Pub Date : 2023-09-05DOI: 10.1134/S0016266323010070
D. V. Gugnin
Three-dimensional manifolds carrying the structure of (n)-valued coset topological groups originating from the Lie groups (Sp(1)) and (SO(3)) are classified.
从李群(Sp(1))和(SO(3))出发，对携带(n) -值协集拓扑群结构的三维流形进行了分类。
{"title":"On the Structure of Coset (n)-Valued Topological Groups on (S^3) and (mathbb{R}P^3)","authors":"D. V. Gugnin","doi":"10.1134/S0016266323010070","DOIUrl":"10.1134/S0016266323010070","url":null,"abstract":"<p> Three-dimensional manifolds carrying the structure of <span>(n)</span>-valued coset topological groups originating from the Lie groups <span>(Sp(1))</span> and <span>(SO(3))</span> are classified. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 1","pages":"71 - 73"},"PeriodicalIF":0.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4233948","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}
Pub Date : 2023-09-05DOI: 10.1134/S0016266323010069
A. Ranjbar-Motlagh
We extend homogeneous and inhomogeneous Nash-type inequalities to abstract metric-measure spaces.
将齐次和非齐次纳什型不等式推广到抽象测度空间。
{"title":"Nash-Type Inequalities on Metric-Measure Spaces","authors":"A. Ranjbar-Motlagh","doi":"10.1134/S0016266323010069","DOIUrl":"10.1134/S0016266323010069","url":null,"abstract":"<p> We extend homogeneous and inhomogeneous Nash-type inequalities to abstract metric-measure spaces. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 1","pages":"65 - 70"},"PeriodicalIF":0.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4235132","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}
Pub Date : 2023-09-05DOI: 10.1134/S0016266323010057
I. A. Proskurnin
There are many papers on the classification of singularities that are invariant or equivariant under the action of a finite group. However, since the problem is difficult, most of these papers consider only special cases, for example, the case of the action of a particular group of small order. In this paper, an attempt is made to prove general statements about equivariantly simple singularities; namely, singularities equivariantly simple with respect to irreducible actions of finite groups are classified. A criterion for the existence of such equivariantly simple singularities is also given.
{"title":"Singularities Equivariantly Simple with Respect to Irreducible Representations","authors":"I. A. Proskurnin","doi":"10.1134/S0016266323010057","DOIUrl":"10.1134/S0016266323010057","url":null,"abstract":"<p> There are many papers on the classification of singularities that are invariant or equivariant under the action of a finite group. However, since the problem is difficult, most of these papers consider only special cases, for example, the case of the action of a particular group of small order. In this paper, an attempt is made to prove general statements about equivariantly simple singularities; namely, singularities equivariantly simple with respect to irreducible actions of finite groups are classified. A criterion for the existence of such equivariantly simple singularities is also given. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 1","pages":"60 - 64"},"PeriodicalIF":0.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4235136","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}
Pub Date : 2023-09-05DOI: 10.1134/S0016266323010082
V. G. Zvyagin, V. P. Orlov
The existence of a weak solution to the initial boundary value problem for the equations of motion of a viscoelastic fluid with memory along the trajectories of a nonsmooth velocity field with inhomogeneous boundary condition is proved. The analysis involves Galerkin-type approximations of the original problem followed by the passage to the limit based on a priori estimates. To study the behavior of trajectories of a nonsmooth velocity field, the theory of regular Lagrangian flows is used.
{"title":"The Weak Solvability of an Inhomogeneous Dynamic Problem for a Viscoelastic Continuum with Memory","authors":"V. G. Zvyagin, V. P. Orlov","doi":"10.1134/S0016266323010082","DOIUrl":"10.1134/S0016266323010082","url":null,"abstract":"<p> The existence of a weak solution to the initial boundary value problem for the equations of motion of a viscoelastic fluid with memory along the trajectories of a nonsmooth velocity field with inhomogeneous boundary condition is proved. The analysis involves Galerkin-type approximations of the original problem followed by the passage to the limit based on a priori estimates. To study the behavior of trajectories of a nonsmooth velocity field, the theory of regular Lagrangian flows is used. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 1","pages":"74 - 79"},"PeriodicalIF":0.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4233949","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}
Pub Date : 2023-09-05DOI: 10.1134/S0016266323010033
J. V. Buralieva
Abelian- and Tauberian-type results characterizing the quasiasymptotic behavior of distributions in (mathcal{S}_{0}'(mathbb{R})) in terms of their Stockwell transforms are obtained. An Abelian-type result relating the quasiasymptotic boundedness of Lizorkin distributions to the asymptotic behavior of their Stockwell transforms is given. Several asymptotic results for the distributional wavelet transform are also presented.
{"title":"Asymptotic Relations for the Distributional Stockwell and Wavelet Transforms","authors":"J. V. Buralieva","doi":"10.1134/S0016266323010033","DOIUrl":"10.1134/S0016266323010033","url":null,"abstract":"<p> Abelian- and Tauberian-type results characterizing the quasiasymptotic behavior of distributions in <span>(mathcal{S}_{0}'(mathbb{R}))</span> in terms of their Stockwell transforms are obtained. An Abelian-type result relating the quasiasymptotic boundedness of Lizorkin distributions to the asymptotic behavior of their Stockwell transforms is given. Several asymptotic results for the distributional wavelet transform are also presented. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 1","pages":"29 - 39"},"PeriodicalIF":0.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4234005","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}
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