Georgian Mathematical Journal最新文献

{"title":"Action of higher derivations on semiprime rings","authors":"Shakir Ali, Vaishali Varshney","doi":"10.1515/gmj-2024-2026","DOIUrl":"https://doi.org/10.1515/gmj-2024-2026","url":null,"abstract":"Let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>m</m:mi> <m:mo>,</m:mo> <m:mi>n</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2026_eq_0341.png\"/> <jats:tex-math>{m,n}</jats:tex-math> </jats:alternatives> </jats:inline-formula> be the fixed positive integers and let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">ℛ</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2026_eq_0224.png\"/> <jats:tex-math>{mathcal{R}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> be a ring. In 1978, Herstein proved that a 2-torsion free prime ring <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"script\">ℛ</m:mi> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2026_eq_0224.png\"/> <jats:tex-math>{mathcal{R}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> is commutative if there is a nonzero derivation <jats:italic>d</jats:italic> of <jats:italic>R</jats:italic> such that <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mo stretchy=\"false\">[</m:mo> <m:mrow> <m:mi>d</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>ϱ</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> <m:mo>,</m:mo> <m:mrow> <m:mi>d</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>ξ</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> <m:mo stretchy=\"false\">]</m:mo> </m:mrow> <m:mo>=</m:mo> <m:mn>0</m:mn> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2026_eq_0157.png\"/> <jats:tex-math>{[d(varrho),d(xi)]=0}</jats:tex-math> </jats:alternatives> </jats:inline-formula> for all <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mi>ϱ</m:mi> <m:mo>,</m:mo> <m:mi>ξ</m:mi> </m:mrow> <m:mo>∈</m:mo> <m:mi>R</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2026_eq_0243.png\"/> <jats:tex-math>{varrho,xiin R}</jats:tex-math> </jats:alternatives> </jats:inline-formula>. In this article, we study the above mentioned classical result for higher derivations and describe the structure of semiprime rings by using the invariance property of prime ideals under higher derivations. Precisely, apart from proving some other important results, we prove the following. Let <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:msub> <m:mi>d</m:mi> <m:mi>i</m:mi> </m:msub> <m:mo stretchy=\"false\">)</m:mo","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":"18 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504361","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":"Dunkl-type Segal–Bargmann transform and its applications to some partial differential equations","authors":"Fethi Soltani, Meriem Nenni","doi":"10.1515/gmj-2024-2031","DOIUrl":"https://doi.org/10.1515/gmj-2024-2031","url":null,"abstract":"In this paper, we give some applications of the Dunkl-type Segal–Bargmann transform <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi mathvariant=\"script\">ℬ</m:mi> <m:mi>α</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2031_eq_0181.png\"/> <jats:tex-math>{mathscr{B}_{alpha}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> in the field of partial differential equations, such as the time-dependent Dunkl–Dirac Laplacian equation and the time-dependent Dunkl–Schrödinger equation. The resolution of these types of problems is based on the techniques of the transmutation operators on the Dunkl-type Fock space <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msub> <m:mi mathvariant=\"script\">ℱ</m:mi> <m:mi>α</m:mi> </m:msub> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:msup> <m:mi>ℂ</m:mi> <m:mi>d</m:mi> </m:msup> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2031_eq_0190.png\"/> <jats:tex-math>{mathscr{F}_{alpha}(mathbb{C}^{d})}</jats:tex-math> </jats:alternatives> </jats:inline-formula>.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":"2 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504360","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 influence of c-subnormality subgroups on the structure of finite groups","authors":"Dana Jaraden, Ali Ateiwi, Jehad Jaraden","doi":"10.1515/gmj-2024-2036","DOIUrl":"https://doi.org/10.1515/gmj-2024-2036","url":null,"abstract":"Let <jats:italic>H</jats:italic> be a subgroup of a group <jats:italic>G</jats:italic>. We say that <jats:italic>H</jats:italic> is <jats:italic>c</jats:italic>-subnormal in <jats:italic>G</jats:italic> if there exists a subnormal subgroup <jats:italic>T</jats:italic> of <jats:italic>G</jats:italic> such that <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mi>H</m:mi> <m:mo>⁢</m:mo> <m:mi>T</m:mi> </m:mrow> <m:mo>=</m:mo> <m:mi>G</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2036_eq_0064.png\"/> <jats:tex-math>{HT=G}</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:mrow> <m:mrow> <m:mi>H</m:mi> <m:mo>∩</m:mo> <m:mi>T</m:mi> </m:mrow> <m:mo>⩽</m:mo> <m:msub> <m:mi>H</m:mi> <m:mi>G</m:mi> </m:msub> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2036_eq_0065.png\"/> <jats:tex-math>{Hcap Tleqslant H_{G}}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>H</m:mi> <m:mi>G</m:mi> </m:msub> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2036_eq_0073.png\"/> <jats:tex-math>{H_{G}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the maximal normal subgroup of <jats:italic>G</jats:italic> which is contained in <jats:italic>H</jats:italic>. In this paper, we investigate the structure of a finite group <jats:italic>G</jats:italic> under the assumption that all maximal subgroups are <jats:italic>c</jats:italic>-subnormal subgroups and present some new conditions for supersolvability.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":"33 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532130","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":"New estimates for the Berezin number of Hilbert space operators","authors":"Parvaneh Zolfaghari","doi":"10.1515/gmj-2024-2012","DOIUrl":"https://doi.org/10.1515/gmj-2024-2012","url":null,"abstract":"In this article, we improve some Berezin number inequalities concerning a Hilbert space. It is shown that if &lt;jats:italic&gt;T&lt;/jats:italic&gt; is a bounded linear operator on a Hilbert space, then for any &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:mrow&gt; &lt;m:mi&gt;r&lt;/m:mi&gt; &lt;m:mo&gt;≥&lt;/m:mo&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;/m:mrow&gt; &lt;/m:math&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2012_eq_0198.png\" /&gt; &lt;jats:tex-math&gt;{rgeq 1}&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;, &lt;jats:disp-formula&gt; &lt;jats:alternatives&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:mrow&gt; &lt;m:msup&gt; &lt;m:mi&gt;𝐛𝐞𝐫&lt;/m:mi&gt; &lt;m:mrow&gt; &lt;m:mn&gt;2&lt;/m:mn&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mi&gt;r&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;/m:msup&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;(&lt;/m:mo&gt; &lt;m:mi&gt;T&lt;/m:mi&gt; &lt;m:mo stretchy=\"false\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;≤&lt;/m:mo&gt; &lt;m:mfrac&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;m:mn&gt;2&lt;/m:mn&gt; &lt;/m:mfrac&gt; &lt;m:msup&gt; &lt;m:mi&gt;𝐛𝐞𝐫&lt;/m:mi&gt; &lt;m:mi&gt;r&lt;/m:mi&gt; &lt;/m:msup&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;(&lt;/m:mo&gt; &lt;m:mo stretchy=\"false\"&gt;|&lt;/m:mo&gt; &lt;m:msup&gt; &lt;m:mi&gt;T&lt;/m:mi&gt; &lt;m:mo&gt;*&lt;/m:mo&gt; &lt;/m:msup&gt; &lt;m:msup&gt; &lt;m:mo stretchy=\"false\"&gt;|&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mn&gt;2&lt;/m:mn&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;m:mo&gt;-&lt;/m:mo&gt; &lt;m:mi&gt;t&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;/m:msup&gt; &lt;m:mo stretchy=\"false\"&gt;|&lt;/m:mo&gt; &lt;m:mi&gt;T&lt;/m:mi&gt; &lt;m:msup&gt; &lt;m:mo stretchy=\"false\"&gt;|&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mn&gt;2&lt;/m:mn&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mi&gt;t&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;/m:msup&gt; &lt;m:mo stretchy=\"false\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;+&lt;/m:mo&gt; &lt;m:mfrac&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;m:mn&gt;4&lt;/m:mn&gt; &lt;/m:mfrac&gt; &lt;m:mo&gt;∥&lt;/m:mo&gt; &lt;m:mo stretchy=\"false\"&gt;|&lt;/m:mo&gt; &lt;m:mi&gt;T&lt;/m:mi&gt; &lt;m:msup&gt; &lt;m:mo stretchy=\"false\"&gt;|&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mn&gt;4&lt;/m:mn&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mi&gt;r&lt;/m:mi&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mi&gt;t&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;/m:msup&gt; &lt;m:mo&gt;+&lt;/m:mo&gt; &lt;m:mo stretchy=\"false\"&gt;|&lt;/m:mo&gt; &lt;m:msup&gt; &lt;m:mi&gt;T&lt;/m:mi&gt; &lt;m:mo&gt;*&lt;/m:mo&gt; &lt;/m:msup&gt; &lt;m:msup&gt; &lt;m:mo stretchy=\"false\"&gt;|&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mn&gt;4&lt;/m:mn&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mi&gt;r&lt;/m:mi&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;m:mo&gt;-&lt;/m:mo&gt; &lt;m:mi&gt;t&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;/m:msup&gt; &lt;m:msub&gt; &lt;m:mo&gt;∥&lt;/m:mo&gt; &lt;m:mi&gt;𝐛𝐞𝐫&lt;/m:mi&gt; &lt;/m:msub&gt; &lt;m:mo mathvariant=\"italic\" separator=\"true\"&gt; &lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;(&lt;/m:mo&gt; &lt;m:mn&gt;0&lt;/m:mn&gt; &lt;m:mo&gt;≤&lt;/m:mo&gt; &lt;m:mi&gt;t&lt;/m:mi&gt; &lt;m:mo&gt;≤&lt;/m:mo&gt; &lt;m:mn&gt;1&lt;/m:mn&gt; &lt;m:mo stretchy=\"false\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;,&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;/m:math&gt; &lt;jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2012_eq_0060.png\" /&gt; &lt;jats:tex-math&gt;mathbf{ber}^{2r}(T)leqfrac{1}{2}mathbf{ber}^{r}({{|{{T}^{*}}|}^{2(1-t)}}{{% |T|}^{2t}})+frac{1}{4}{{|{{|T|}^{4rt}}+{{|{{T}^{*}}|}^{4r(1-t)}}|}_{mathbf% {ber}}}quad(0leq tleq 1),&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:disp-formula&gt; where &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:mrow&gt; &lt;m:mrow&gt; &lt;m:mo ","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":"29 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299181","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 generalized derivations in factor rings","authors":"Mohammed Zerra, Karim Bouchannafa, Lahcen Oukhtite","doi":"10.1515/gmj-2024-2017","DOIUrl":"https://doi.org/10.1515/gmj-2024-2017","url":null,"abstract":"The main purpose of this paper is to scrutinize the deportment of generalized derivations of <jats:italic>R</jats:italic> satisfying some functional <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mo>*</m:mo> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2017_eq_0051.png\" /> <jats:tex-math>{*}</jats:tex-math> </jats:alternatives> </jats:inline-formula>-identities involving the center of the factor ring <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>R</m:mi> <m:mo>/</m:mo> <m:mi>P</m:mi> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2017_eq_0081.png\" /> <jats:tex-math>{R/P}</jats:tex-math> </jats:alternatives> </jats:inline-formula> where <jats:italic>P</jats:italic> is a prime ideal of the ring <jats:italic>R</jats:italic>. Moreover, we suggest to give generalization of some well known results.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":"17 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299509","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":"Group invertibility of the sum in rings and its applications","authors":"Huanyin Chen, Dayong Liu, Marjan Sheibani","doi":"10.1515/gmj-2024-2010","DOIUrl":"https://doi.org/10.1515/gmj-2024-2010","url":null,"abstract":"We present necessary and sufficient conditions under which the sum of two group invertible elements in a ring is group invertible. As applications, we establish the existence of group inverses of certain <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mn>2</m:mn> <m:mo>×</m:mo> <m:mn>2</m:mn> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2010_eq_0193.png\" /> <jats:tex-math>{2times 2}</jats:tex-math> </jats:alternatives> </jats:inline-formula> block-operator matrices over a Banach space. These generalize the known results, e.g., Zhou, Chen and Zhu (<jats:italic>Comm. Algebra</jats:italic> 48 (2020), 676–690) and Benítez, Liu and Zhu (<jats:italic>Linear Multilinear Algebra</jats:italic> 59 (2011), 279–289).","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":"2016 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299185","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":"Generalized Stockwell transforms: Spherical mean operators and applications","authors":"Saifallah Ghobber, Hatem Mejjaoli","doi":"10.1515/gmj-2024-2014","DOIUrl":"https://doi.org/10.1515/gmj-2024-2014","url":null,"abstract":"The spherical mean operator has been widely studied and has seen remarkable development in many areas of harmonic analysis. In this paper, we consider the Stockwell transform related to the spherical mean operator. Since the study of time-frequency analysis is both theoretically interesting and practically useful, we will study several problems for the generalized Stockwell transform. Firstly, we explore the Shapiro uncertainty principle for this transformation. Next, we will study the boundedness and then the compactness of localization operators related to the generalized Stockwell transform, and finally we will introduce and study its scalogram.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299186","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":"Weak type estimates of genuine Calderón–Zygmund operators on the local Morrey spaces associated with ball quasi-Banach function spaces","authors":"Mingwei Shi, Jiang Zhou, Songbai Wang","doi":"10.1515/gmj-2024-2013","DOIUrl":"https://doi.org/10.1515/gmj-2024-2013","url":null,"abstract":"Weak type estimates for genuine Calderón–Zygmund operators are established on the local Morrey spaces associated with ball quasi-Banach function spaces by two different methods. Above all, we obtain weak type estimates for the operator on the local weak Morrey spaces with variable exponents.","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":"21 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299212","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":"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":"61 1","pages":""},"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 &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:mrow&gt; &lt;m:msup&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:mi&gt;A&lt;/m:mi&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mi&gt;B&lt;/m:mi&gt; &lt;/m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;†&lt;/m:mo&gt; &lt;/m:msup&gt; &lt;m:mo&gt;=&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:msup&gt; &lt;m:mi&gt;B&lt;/m:mi&gt; &lt;m:mo&gt;∗&lt;/m:mo&gt; &lt;/m:msup&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:msup&gt; &lt;m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;(&lt;/m:mo&gt; &lt;m:mrow&gt; &lt;m:msup&gt; &lt;m:mi&gt;A&lt;/m:mi&gt; &lt;m:mo&gt;∗&lt;/m:mo&gt; &lt;/m:msup&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mi&gt;A&lt;/m:mi&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:mi&gt;B&lt;/m:mi&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:msup&gt; &lt;m:mi&gt;B&lt;/m:mi&gt; &lt;m:mo&gt;∗&lt;/m:mo&gt; &lt;/m:msup&gt; &lt;/m:mrow&gt; &lt;m:mo stretchy=\"false\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mi mathvariant=\"normal\"&gt;#&lt;/m:mi&gt; &lt;/m:msup&gt; &lt;m:mo&gt;⁢&lt;/m:mo&gt; &lt;m:msup&gt; &lt;m:mi&gt;A&lt;/m:mi&gt; &lt;m:mo&gt;∗&lt;/m:mo&gt; &lt;/m:msup&gt; &lt;/m:mrow&gt; &lt;/m:mrow&gt; &lt;/m:math&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2016_eq_0486.png\" /&gt; &lt;jats:tex-math&gt;{(AB)^{{dagger}}=B^{ast}(A^{ast}ABB^{ast})^{#}A^{ast}}&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;, and show that this matrix equality always holds through the use of a special matrix rank equality and some matrix range operations, where &lt;jats:italic&gt;A&lt;/jats:italic&gt; and &lt;jats:italic&gt;B&lt;/jats:italic&gt; are two matrices of appropriate sizes, &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:msup&gt; &lt;m:mrow&gt; &lt;m:mo rspace=\"4.2pt\" stretchy=\"false\"&gt;(&lt;/m:mo&gt; &lt;m:mo rspace=\"4.2pt\"&gt;⋅&lt;/m:mo&gt; &lt;m:mo stretchy=\"false\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;∗&lt;/m:mo&gt; &lt;/m:msup&gt; &lt;/m:math&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2016_eq_0509.png\" /&gt; &lt;jats:tex-math&gt;{(,cdot,)^{ast}}&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;, &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:msup&gt; &lt;m:mrow&gt; &lt;m:mo rspace=\"4.2pt\" stretchy=\"false\"&gt;(&lt;/m:mo&gt; &lt;m:mo rspace=\"4.2pt\"&gt;⋅&lt;/m:mo&gt; &lt;m:mo stretchy=\"false\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mo&gt;†&lt;/m:mo&gt; &lt;/m:msup&gt; &lt;/m:math&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2016_eq_0510.png\" /&gt; &lt;jats:tex-math&gt;{(,cdot,)^{{dagger}}}&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; and &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;m:msup&gt; &lt;m:mrow&gt; &lt;m:mo rspace=\"4.2pt\" stretchy=\"false\"&gt;(&lt;/m:mo&gt; &lt;m:mo rspace=\"4.2pt\"&gt;⋅&lt;/m:mo&gt; &lt;m:mo stretchy=\"false\"&gt;)&lt;/m:mo&gt; &lt;/m:mrow&gt; &lt;m:mi mathvariant=\"normal\"&gt;#&lt;/m:mi&gt; &lt;/m:msup&gt; &lt;/m:math&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_gmj-2024-2016_eq_0508.png\" /&gt; &lt;jats:tex-math&gt;{(,cdot,)^{#}}&lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; mean the conjugate transpose, the Moor","PeriodicalId":55101,"journal":{"name":"Georgian Mathematical Journal","volume":"104 1","pages":""},"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}