Siberian Mathematical Journal最新文献

{"title":"Weighted Composition Operators on Quasi-Banach Weighted Sequence Spaces","authors":"A. V. Abanin, R. S. Mannanikov","doi":"10.1134/s0037446624040165","DOIUrl":"https://doi.org/10.1134/s0037446624040165","url":null,"abstract":"<p>This paper studies the basic topological properties of weighted composition operators\u0000on the weighted sequence spaces <span>( l^{p}(operatorname{w}) )</span>, with <span>( 0&lt;p&lt;infty )</span>,\u0000given by a weight sequence <span>( operatorname{w} )</span> of positive reals\u0000such as boundedness, compactness, compactness of differences of two operators, formulas for their essential norms,\u0000and description of closed range operators.\u0000Previously these properties were studied by Luan and Khoi in the case of Hilbert space <span>( (p=2) )</span>.\u0000Their methods can be also applied with some minor modifications to the case of Banach spaces <span>( l^{p}(operatorname{w}) )</span>\u0000with <span>( p&gt;1 )</span>.\u0000They based essentially on using the dual spaces of continuous linear functionals and, consequently,\u0000cannot be applied to the quasi-Banach case <span>( (0&lt;p&lt;1) )</span>. Moreover, some of them do not work even\u0000in <span>( l^{1}(operatorname{w}) )</span>.\u0000Motivated by these reasons, we develop a more universal approach that allows studying\u0000the whole scale of spaces <span>( {l^{p}(operatorname{w}):p&gt;0} )</span>.\u0000To this end, we establish the necessary and sufficient conditions for a linear operator to be compact\u0000on an abstract quasi-Banach sequence space. These conditions are new even in the case of Banach spaces.\u0000Moreover, we introduce the new characteristic, the <span>( omega )</span>-essential norm of a continuous linear operator <span>( L )</span>\u0000on a quasi-Banach space <span>( X )</span>.\u0000This characteristic measures the distance in the operator metric, between <span>( L )</span> and the set of all <span>( omega )</span>-compact operators on <span>( X )</span>.\u0000Here an operator <span>( K )</span> is <span>( omega )</span>-compact on <span>( X )</span> if <span>( K )</span> is compact and coordinatewise continuous on <span>( X )</span>.\u0000We show that for <span>( l^{p}(operatorname{w}) )</span> with <span>( p&gt;1 )</span> the essential and <span>( omega )</span>-essential norms\u0000of a weighted composition operator coincide, whereas for <span>( 0&lt;pleq 1 )</span> we do not know whether the same is true or not.\u0000Our main results for weighted composition operators in <span>( l^{p}(operatorname{w}) )</span> <span>( (0&lt;p&lt;infty) )</span> are as follows:\u0000We provide criteria for an operator to be bounded, compact, or closed range, and completely describe the pairs of operators\u0000with compact difference; as well as some exact formula for the <span>( omega )</span>-essential norm. Some key aspects of\u0000our approach can be used for other operators\u0000and scales of spaces.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"38 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141718502","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}

{"title":"Integration of the Modified Korteweg-de Vries Equation with Time-Dependent Coefficients and a Self-Consistent Source","authors":"Sh. K. Sobirov, U. A. Hoitmetov","doi":"10.1134/s0037446624040220","DOIUrl":"https://doi.org/10.1134/s0037446624040220","url":null,"abstract":"<p>We consider the Cauchy problem for the modified Korteweg-de Vries equation\u0000with time-dependent coefficients and a self-consistent source in the class of rapidly decreasing functions.\u0000To solve the problem, we find Lax pairs and employ the inverse scattering method.\u0000Note that in the case under study the Dirac operator is not selfadjoint, and so the eigenvalues can be multiples.\u0000We find the equations describing the dynamics in time of the scattering data of a nonselfadjoint Dirac operator\u0000whose potential is a solution to the modified Korteweg-de Vries equation with time-dependent coefficients\u0000and a self-consistent source in the class of rapidly decreasing functions.\u0000As a special case,\u0000we examine a loaded modified Korteweg-de Vries equation with a self-consistent source.\u0000The equations describe the dynamics in time of the scattering data of a nonselfadjoint Dirac operator\u0000whose potential is a solution to the loaded modified Korteweg-de Vries equation with variable coefficients\u0000in the class of rapidly decreasing functions.\u0000We provide some examples that illustrate applications of the results.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"77 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141722157","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}

{"title":"The Inverse Problem for the Heat Equation with Two Unknown Coefficients","authors":"M. R. Ishmeev","doi":"10.1134/s0037446624030170","DOIUrl":"https://doi.org/10.1134/s0037446624030170","url":null,"abstract":"<p>We solve the simultaneous recovery of thermal conductivity and a high-frequency coefficient of a source\u0000in a one-dimensional initial-boundary value problem for the heat equation with\u0000Dirichlet boundary conditions and an inhomogeneous initial condition\u0000from some information on the partial asymptotics of a solution. We show\u0000that the coefficients can be restored from some data on the asymptotics of a solution,\u0000which is constructed and justified.\u0000This article was inspired by Denisov’s research on a variety of inverse\u0000problems without accounting for high-frequency oscillations.\u0000Also, we continue the research by Levenshtam and his students which firstly\u0000addressed the inverse problems for parabolic equations with high-frequency coefficients and developed the relevant\u0000methodology. In contrast to\u0000the previous research of the case that only the source function or its factors are unknown,\u0000we assume that the thermal conductivity and the factor of a source function\u0000are unknown simultaneously.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"14 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169483","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}

{"title":"On Regular Subgroups in  $ operatorname{Lim}(N) $","authors":"N. M. Suchkov, A. A. Shlepkin","doi":"10.1134/s0037446624030121","DOIUrl":"https://doi.org/10.1134/s0037446624030121","url":null,"abstract":"<p>Let <span>( G )</span> be the group of all limited permutations of the set of naturals.\u0000We prove that every countable locally finite group is isomorphic to some regular\u0000subgroup of <span>( G )</span>. Also, if a regular subgroup <span>( H )</span> of <span>( G )</span> contains an element\u0000of infinite order then <span>( H )</span> has a normal infinite cyclic subgroup of finite index.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"97 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169558","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}

{"title":"ITBM-Constructive Completions of Algebras","authors":"A. S. Morozov","doi":"10.1134/s003744662403008x","DOIUrl":"https://doi.org/10.1134/s003744662403008x","url":null,"abstract":"<p>We introduce the notion of ITBM-constructive algebra, which is a generalization of the notion of constructive algebra,\u0000and study completions of such algebras.\u0000We obtain some criterion for the existence of completions for metrized algebras\u0000and prove that each ITBM-constructive metrized algebra\u0000which has completion can be naturally extended to the ITBM-constructive\u0000completion. Using these results, we establish the existence of\u0000ITBM-constructive presentations for some particular algebras.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"41 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169605","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}

{"title":"An Example of a Relatively Maximal Nonpronormal Subgroup of Odd Order in a Finite Simple Group","authors":"X. Zhang, L. Su, D. O. Revin","doi":"10.1134/s0037446624030133","DOIUrl":"https://doi.org/10.1134/s0037446624030133","url":null,"abstract":"<p>We prove the existence of a triple <span>( ({mathfrak{X}},G,H) )</span>, where <span>( {mathfrak{X}} )</span>\u0000is a class of finite groups consisting of groups of odd order which is complete\u0000(i.e., closed under subgroups, homomorphic images, and extensions),\u0000<span>( G )</span> is a finite simple group, <span>( H )</span> is an <span>( {mathfrak{X}} )</span>-maximal subgroup in <span>( G )</span>,\u0000and <span>( H )</span> is not pronormal in <span>( G )</span>.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"18 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169492","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}

{"title":"Constructions of Quandles over Groups and Rings","authors":"A. A. Simonov, M. V. Neshchadim, A. N. Borodin","doi":"10.1134/s003744662403011x","DOIUrl":"https://doi.org/10.1134/s003744662403011x","url":null,"abstract":"<p>We present the following constructions: extension of a trivial quandle\u0000by a group with a nontrivial abelian subgroup,\u0000a quandle over a noncommutative group\u0000by an arbitrary antiautomorphism,\u0000a quandle presenting from a generalized Alexander quandle\u0000with the replacement of the automorphism by a central antiautomorphism, and\u0000a quandle over an <span>( n )</span>-dimensional module\u0000depending on <span>( n(n-1)-1 )</span>\u0000parameters with <span>( ngeq 2 )</span> in a commutative unital ring.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"42 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169496","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}

{"title":"A Coercive Estimate for the Nonhomogeneous Differential Operator on the Heisenberg Group","authors":"D. V. Isangulova","doi":"10.1134/s0037446624030157","DOIUrl":"https://doi.org/10.1134/s0037446624030157","url":null,"abstract":"<p>We construct some linear nonhomogeneous differential operator <span>( mathcal{Q} )</span> on the Heisenberg group\u0000whose kernel is interconnected with the Lie algebra of the group of conformal mappings.\u0000In more detail, the kernel of <span>( mathcal{Q} )</span> coincides with first two coordinate functions of mappings of\u0000the Lie algebra of conformal mappings.\u0000We derive the integral representation formula and\u0000give a coercive estimate for <span>( mathcal{Q} )</span>.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"22 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169557","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}

{"title":"On Isomorphic Embeddings in the Class of Disjointly Homogeneous Rearrangement Invariant Spaces","authors":"S. V. Astashkin","doi":"10.1134/s0037446624030017","DOIUrl":"https://doi.org/10.1134/s0037446624030017","url":null,"abstract":"<p>The equivalence of the Haar system in a rearrangement\u0000invariant space <span>( X )</span> on <span>( [0,1] )</span> and a sequence of pairwise disjoint functions\u0000in some Lorentz space is known to imply that <span>( X=L_{2}[0,1] )</span> up to the equivalence of\u0000norms. We show that the same holds for the class of uniform\u0000disjointly homogeneous rearrangement invariant spaces and obtain a few\u0000consequences for the properties of isomorphic embeddings of such spaces.\u0000In particular, the <span>( L_{p}[0,1] )</span> space with <span>( 1&lt;p&lt;infty )</span> is the\u0000only uniform <span>( p )</span>-disjointly homogeneous rearrangement invariant space on <span>( [0,1] )</span>\u0000with nontrivial Boyd indices which has two rearrangement invariant representations\u0000on the half-axis <span>( (0,infty) )</span>.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"49 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169855","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}

{"title":"Boundary Values in the Geometric Function Theory in Domains with Moving Boundaries","authors":"S. K. Vodopyanov, S. V. Pavlov","doi":"10.1134/s0037446624030054","DOIUrl":"https://doi.org/10.1134/s0037446624030054","url":null,"abstract":"<p>This article addresses the problem of boundary correspondence\u0000for a sequence of homeomorphisms that\u0000change the capacity of a condenser in a controlled way.\u0000To study the overall boundary behavior of these mappings,\u0000we introduce some capacity metrics\u0000in a sequence of domains with nondegenerate core.\u0000Completions with respect to these metrics add to the domains new points called boundary elements.\u0000As one of the consequences, we obtain not only sufficient conditions for\u0000the global uniform convergence of a sequence of homeomorphisms,\u0000but some applications to elasticity theory as well.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"2016 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169479","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}