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":null,"pages":null},"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":null,"pages":null},"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":"On Locally Finite Groups Saturated by Full and Special Linear Groups over Finite Fields","authors":"A. Shlepkin","doi":"10.1134/s003744662404013x","DOIUrl":"https://doi.org/10.1134/s003744662404013x","url":null,"abstract":"","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141714806","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":"Asymptotics of Solutions to a Third-Order Equation in a Neighborhood of an Irregular Singular Point","authors":"M. Korovina, H. Matevossian, I. N. Smirnov","doi":"10.1134/s0037446624040177","DOIUrl":"https://doi.org/10.1134/s0037446624040177","url":null,"abstract":"","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141691570","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":"Finite Groups with $ G $-Permutable Normalizers of Sylow Subgroups","authors":"S. Kamornikov, V. N. Tyutyanov, O. Shemetkova","doi":"10.1134/s0037446624040049","DOIUrl":"https://doi.org/10.1134/s0037446624040049","url":null,"abstract":"","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141689292","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":"Inequalities for a Rational Function with Prescribed Poles","authors":"A. Mir, T. Fayaz","doi":"10.1134/s0037446624040153","DOIUrl":"https://doi.org/10.1134/s0037446624040153","url":null,"abstract":"","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141703630","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":"Identification of the Heat Transfer Coefficient from Boundary Integral Data","authors":"S. G. Pyatkov, O. Soldatov","doi":"10.1134/s0037446624040104","DOIUrl":"https://doi.org/10.1134/s0037446624040104","url":null,"abstract":"","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141700239","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 Absence of Global Solutions of a Fourth-Order Gauss Type Equation","authors":"A. V. Neklyudov","doi":"10.1134/s0037446624040190","DOIUrl":"https://doi.org/10.1134/s0037446624040190","url":null,"abstract":"","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141689080","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 Multidimensional Analog of the Conway Circle","authors":"S. A. Malyugin","doi":"10.1134/s0037446624040086","DOIUrl":"https://doi.org/10.1134/s0037446624040086","url":null,"abstract":"","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141716800","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":"Finite Groups with Systems of Generalized Normal Subgroups","authors":"A.-M. Liu, S. Wang, V. G. Safonov, A. N. Skiba","doi":"10.1134/s0037446624040062","DOIUrl":"https://doi.org/10.1134/s0037446624040062","url":null,"abstract":"","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141705983","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}