Georgian Mathematical Journal最新文献

{"title":"σ-symmetric amenability of Banach algebras","authors":"Lin Chen, Mohammad Javad Mehdipour, Jun Li","doi":"10.1515/gmj-2024-2011","DOIUrl":"https://doi.org/10.1515/gmj-2024-2011","url":null,"abstract":"In this paper, we introduce the notion of σ-symmetric amenability of Banach algebras and investigate some hereditary properties of them. We also apply our results to several abstract Segal algebras and group algebras.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299183","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 and characterizations of mixed reverse-order laws for the Moore–Penrose inverse and group inverse","authors":"Yongge Tian","doi":"10.1515/gmj-2024-2016","DOIUrl":"https://doi.org/10.1515/gmj-2024-2016","url":null,"abstract":"This paper is concerned with constructions and characterizations of matrix equalities that involve mixed products of Moore–Penrose inverses and group inverses of two matrices. We first construct a mixed reverse-order law <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msup> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mi>A</m:mi> <m:mo>⁢</m:mo> <m:mi>B</m:mi> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mo>†</m:mo> </m:msup> <m:mo>=</m:mo> <m:mrow> <m:msup> <m:mi>B</m:mi> <m:mo>∗</m:mo> </m:msup> <m:mo>⁢</m:mo> <m:msup> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:msup> <m:mi>A</m:mi> <m:mo>∗</m:mo> </m:msup> <m:mo>⁢</m:mo> <m:mi>A</m:mi> <m:mo>⁢</m:mo> <m:mi>B</m:mi> <m:mo>⁢</m:mo> <m:msup> <m:mi>B</m:mi> <m:mo>∗</m:mo> </m:msup> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mi mathvariant=\"normal\">#</m:mi> </m:msup> <m:mo>⁢</m:mo> <m:msup> <m:mi>A</m:mi> <m:mo>∗</m:mo> </m:msup> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2016_eq_0486.png\" /> <jats:tex-math>{(AB)^{{dagger}}=B^{ast}(A^{ast}ABB^{ast})^{#}A^{ast}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, and show that this matrix equality always holds through the use of a special matrix rank equality and some matrix range operations, where <jats:italic>A</jats:italic> and <jats:italic>B</jats:italic> are two matrices of appropriate sizes, <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mo rspace=\"4.2pt\" stretchy=\"false\">(</m:mo> <m:mo rspace=\"4.2pt\">⋅</m:mo> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mo>∗</m:mo> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2016_eq_0509.png\" /> <jats:tex-math>{(,cdot,)^{ast}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mo rspace=\"4.2pt\" stretchy=\"false\">(</m:mo> <m:mo rspace=\"4.2pt\">⋅</m:mo> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mo>†</m:mo> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2016_eq_0510.png\" /> <jats:tex-math>{(,cdot,)^{{dagger}}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mo rspace=\"4.2pt\" stretchy=\"false\">(</m:mo> <m:mo rspace=\"4.2pt\">⋅</m:mo> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mi mathvariant=\"normal\">#</m:mi> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2016_eq_0508.png\" /> <jats:tex-math>{(,cdot,)^{#}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> mean the conjugate transpose, the Moor","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299182","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":"Analytic solution to functional differential equations via Bell’s polynomials","authors":"Diego Caratelli, Pierpaolo Natalini, Paolo Emilio Ricci","doi":"10.1515/gmj-2024-2005","DOIUrl":"https://doi.org/10.1515/gmj-2024-2005","url":null,"abstract":"It is shown how to approximate the solution of functional differential equations in terms of Bell’s polynomials. Some numerical checks are shown, by using the computer algebra system Mathematica<jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi /> <m:mi mathvariant=\"normal\">©</m:mi> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2005_eq_0181.png\" /> <jats:tex-math>{{}^{copyright}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139918098","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":"Degeneration phenomenon in linear ordinary differential equations","authors":"Vakhtang Lomadze","doi":"10.1515/gmj-2024-2007","DOIUrl":"https://doi.org/10.1515/gmj-2024-2007","url":null,"abstract":"Given a linear constant coefficient ODE depending on a parameter, when this parameter approaches zero, the solution set converges to the solution set of the limit differential equation if the leading coefficient does not vanish. The situation is very subtle in the singular case, i.e., in the case when this coefficient becomes zero. The solution set then may even collapse completely. In this note, a formalism is developed in which the solution set of a linear constant coefficient ODE always depends continuously on the equation coefficients.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139918169","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 perturbation of continuous frames in Hilbert C *-modules","authors":"Hadi Ghasemi, Tayebe Lal Shateri","doi":"10.1515/gmj-2023-2111","DOIUrl":"https://doi.org/10.1515/gmj-2023-2111","url":null,"abstract":"In the present paper, we examine the perturbation of continuous frames and Riesz-type frames in Hilbert <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>C</m:mi> <m:mo>*</m:mo> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2111_eq_0167.png\" /> <jats:tex-math>{C^{*}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-modules. We extend the Casazza–Christensen general perturbation theorem for Hilbert space frames to continuous frames in Hilbert <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>C</m:mi> <m:mo>*</m:mo> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2111_eq_0167.png\" /> <jats:tex-math>{C^{*}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-modules. We obtain a necessary condition under which the perturbation of a Riesz-type frame of Hilbert <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>C</m:mi> <m:mo>*</m:mo> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2111_eq_0167.png\" /> <jats:tex-math>{C^{*}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-modules remains to be a Riesz-type frame. Also, we examine the effect of duality on the perturbation of continuous frames in Hilbert <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>C</m:mi> <m:mo>*</m:mo> </m:msup> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2023-2111_eq_0167.png\" /> <jats:tex-math>{C^{*}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-modules, and we prove that if the operator frame of a continuous frame <jats:italic>F</jats:italic> is near to the combination of the synthesis operator of a continuous Bessel mapping <jats:italic>G</jats:italic> and the analysis operator of <jats:italic>F</jats:italic>, then <jats:italic>G</jats:italic> is a continuous frame.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139918315","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 generalization of Hardy’s inequality to infinite tensors","authors":"Morteza Saheli, Davoud Foroutannia, Sara Yusefian","doi":"10.1515/gmj-2024-2006","DOIUrl":"https://doi.org/10.1515/gmj-2024-2006","url":null,"abstract":"In this paper, we extend Hardy’s inequality to infinite tensors. To do so, we introduce Cesàro tensors <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>ℭ</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2006_eq_0150.png\" /> <jats:tex-math>{mathfrak{C}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, and consider them as tensor maps from sequence spaces into tensor spaces. In fact, we prove inequalities of the form <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msub> <m:mrow> <m:mo>∥</m:mo> <m:mrow> <m:mi>ℭ</m:mi> <m:mo>⁢</m:mo> <m:msup> <m:mi>x</m:mi> <m:mi>k</m:mi> </m:msup> </m:mrow> <m:mo>∥</m:mo> </m:mrow> <m:mrow> <m:mi>t</m:mi> <m:mo>,</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>≤</m:mo> <m:mrow> <m:mi>U</m:mi> <m:mo>⁢</m:mo> <m:msubsup> <m:mrow> <m:mo>∥</m:mo> <m:mi>x</m:mi> <m:mo>∥</m:mo> </m:mrow> <m:msub> <m:mi>l</m:mi> <m:mi>p</m:mi> </m:msub> <m:mi>k</m:mi> </m:msubsup> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2006_eq_0106.png\" /> <jats:tex-math>|mathfrak{C}x^{k}|_{t,1}leq U|x|_{l_{p}}^{k}</jats:tex-math> </jats:alternatives> </jats:inline-formula> (<jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>k</m:mi> <m:mo>=</m:mo> <m:mrow> <m:mn>1</m:mn> <m:mo>,</m:mo> <m:mn>2</m:mn> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2006_eq_0107.png\" /> <jats:tex-math>k=1,2</jats:tex-math> </jats:alternatives> </jats:inline-formula>), where <jats:italic>x</jats:italic> is a sequence, <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>ℭ</m:mi> <m:mo>⁢</m:mo> <m:msup> <m:mi>x</m:mi> <m:mi>k</m:mi> </m:msup> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2006_eq_0149.png\" /> <jats:tex-math>{mathfrak{C}x^{k}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> is a tensor, and <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo>∥</m:mo> <m:mo>⋅</m:mo> <m:msub> <m:mo>∥</m:mo> <m:mrow> <m:mi>t</m:mi> <m:mo>,</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msub> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2006_eq_0155.png\" /> <jats:tex-math>{|cdot|_{t,1}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo>∥</m:mo> <m:mo>⋅</m:mo> <m:msub> <m:mo>∥</m:mo> <m:msub> <m:mi>l</m:mi> <m:mi>p</m:mi> </m:msub> </m:msub> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139918167","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":"Busemann--Petty-type problem for μ-intersection bodies","authors":"Chao Li, Gangyi Chen","doi":"10.1515/gmj-2024-2009","DOIUrl":"https://doi.org/10.1515/gmj-2024-2009","url":null,"abstract":"The Busemann–Petty problem of arbitrary measure for symmetric star bodies is proposed and studied by Zvavitch, which is a generalization of the classical Busemann–Petty problem. In this paper, we study the Busemann–Petty-type problem for homogeneous measure for general star bodies.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139918317","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":"Fractional p-Laplacian elliptic Dirichlet problems","authors":"David Barilla, Martin Bohner, Giuseppe Caristi, Fariba Gharehgazlouei, Shapour Heidarkhani","doi":"10.1515/gmj-2024-2008","DOIUrl":"https://doi.org/10.1515/gmj-2024-2008","url":null,"abstract":"In this paper, we consider a fractional <jats:italic>p</jats:italic>-Laplacian elliptic Dirichlet problem that possesses one control parameter and has a Lipschitz nonlinearity order of <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>p</m:mi> <m:mo>-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2008_eq_0274.png\" /> <jats:tex-math>{p-1}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. The multiplicity of the weak solutions is proved by means of the variational method and critical point theory. We investigate the existence of at least three solutions to the problem.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139918316","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 the correspondence between periodic solutions of differential and dynamic equations on periodic time scales","authors":"Viktoriia Tsan, Oleksandr Stanzhytskyi, Olha Martynyuk","doi":"10.1515/gmj-2024-2003","DOIUrl":"https://doi.org/10.1515/gmj-2024-2003","url":null,"abstract":"This paper studies the relationship between the existence of periodic solutions of systems of dynamic equations on time scales and their corresponding systems of differential equations. We have established that, for a sufficiently small graininess function, if a dynamic equation on a time scale has an asymptotically stable periodic solution, then the corresponding differential equation will also have a periodic solution. A converse result has also been obtained, where the existence of a periodic solution of a differential equation implies the existence of a corresponding solution on time scales, provided that the graininess function is sufficiently small.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139771538","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":"V_a -deformed free convolution and variance function","authors":"Raouf Fakhfakh","doi":"10.1515/gmj-2024-2004","DOIUrl":"https://doi.org/10.1515/gmj-2024-2004","url":null,"abstract":"In this paper, we deal with the notion of <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>V</m:mi> <m:mi>a</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2004_eq_0134.png\" /> <jats:tex-math>{V_{a}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-deformed free convolution, introduced in [A. D. Krystek and L. J. Wojakowski, Associative convolutions arising from conditionally free convolution, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 8 2005, 3, 515–545], from a point of view related to the theory of Cauchy–Stieltjes kernel (CSK) families and their corresponding variance functions. We determine the formula for variance function under a power of <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>V</m:mi> <m:mi>a</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2004_eq_0134.png\" /> <jats:tex-math>{V_{a}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-deformed free convolution. Then we provide an approximation of elements of the CSK family generated by <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>V</m:mi> <m:mi>a</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2004_eq_0134.png\" /> <jats:tex-math>{V_{a}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-deformed free Poisson distribution.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139658777","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}