{"title":"Invariant mean value property and $mathcal M$-harmonicity on the half-space","authors":"B. Choe, Kyesook Nam","doi":"10.4134/BKMS.B200023","DOIUrl":"https://doi.org/10.4134/BKMS.B200023","url":null,"abstract":"","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"58 1","pages":"559-572"},"PeriodicalIF":0.5,"publicationDate":"2021-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41910166","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}
The convex hull of a generic triple of boundary points has non-zero finite volume in complex hyperbolic 2-space.
一般三重边值点的凸包在复双曲2-空间中具有非零有限体积。
{"title":"The convex hull of three boundary points in complex hyperbolic space","authors":"Young-Jin Kim","doi":"10.4134/BKMS.B200492","DOIUrl":"https://doi.org/10.4134/BKMS.B200492","url":null,"abstract":"The convex hull of a generic triple of boundary points has non-zero finite volume in complex hyperbolic 2-space.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"58 1","pages":"721-727"},"PeriodicalIF":0.5,"publicationDate":"2021-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43854947","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 ampliation quasiaffine transforms of operators","authors":"E. Ko","doi":"10.4134/BKMS.B200473","DOIUrl":"https://doi.org/10.4134/BKMS.B200473","url":null,"abstract":"","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"58 1","pages":"699-710"},"PeriodicalIF":0.5,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42642197","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}
We prove existence and regularity results of solutions for a class of nonlinear singular elliptic problems like − div ( (a(x) + |u|)∇u ) = f |u|γ in Ω, u = 0 on ∂Ω, where Ω is a bounded open subset of RN(N ≥ 2), a(x) is a measurable nonnegative function, q, γ > 0 and the source f is a nonnegative (not identicaly zero) function belonging to Lm(Ω) for some m ≥ 1. Our results will depend on the summability of f and on the values of q, γ > 0.
{"title":"On nonlinear elliptic equations with singular lower order term","authors":"A. Marah, H. Redwane","doi":"10.4134/BKMS.B200311","DOIUrl":"https://doi.org/10.4134/BKMS.B200311","url":null,"abstract":"We prove existence and regularity results of solutions for a class of nonlinear singular elliptic problems like − div ( (a(x) + |u|)∇u ) = f |u|γ in Ω, u = 0 on ∂Ω, where Ω is a bounded open subset of RN(N ≥ 2), a(x) is a measurable nonnegative function, q, γ > 0 and the source f is a nonnegative (not identicaly zero) function belonging to Lm(Ω) for some m ≥ 1. Our results will depend on the summability of f and on the values of q, γ > 0.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"58 1","pages":"385-401"},"PeriodicalIF":0.5,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43215047","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}
We examine the theory of surfaces in the isotropic threespace, with emphases on the surfaces related to the zero mean curvature.
我们研究了各向同性三维空间中的曲面理论,重点是与零平均曲率相关的曲面。
{"title":"Zero mean curvature surfaces in isotropic three-space","authors":"J. Seo, Seong-Deog Yang","doi":"10.4134/BKMS.B190783","DOIUrl":"https://doi.org/10.4134/BKMS.B190783","url":null,"abstract":"We examine the theory of surfaces in the isotropic threespace, with emphases on the surfaces related to the zero mean curvature.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"58 1","pages":"1-20"},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70362880","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}
For pseudo-free and recurrent self-similar groups, we show that continuous orbit equivalence of inverse semigroup partial actions implies continuous orbit equivalence of group actions. Conversely, if group actions are continuous orbit equivalent, and the induced homeomorphism commutes with the shift maps on their groupoids, we obtain continuous orbit equivalence of inverse semigroup partial actions.
{"title":"CONTINUOUS ORBIT EQUIVALENCES ON SELF-SIMILAR GROUPS","authors":"Inhyeop Yi","doi":"10.4134/BKMS.B200055","DOIUrl":"https://doi.org/10.4134/BKMS.B200055","url":null,"abstract":"For pseudo-free and recurrent self-similar groups, we show that continuous orbit equivalence of inverse semigroup partial actions implies continuous orbit equivalence of group actions. Conversely, if group actions are continuous orbit equivalent, and the induced homeomorphism commutes with the shift maps on their groupoids, we obtain continuous orbit equivalence of inverse semigroup partial actions.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"28 8 1","pages":"133-146"},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70363222","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}
In this paper, we decompose (under unitary similarity) the Kronecker sum A A (= A⊗ I + I ⊗A) into a direct sum of irreducible matrices, when A is a 3×3 matrix. As a consequence we identify K(A A) as the direct sum of several full matrix algebras as predicted by Artin– Wedderburn theorem, where K(T ) is the unital algebra generated by T and T ∗.
{"title":"DECOMPOSITION OF THE KRONECKER SUMS OF MATRICES INTO A DIRECT SUM OF IRREDUCIBLE MATRICES","authors":"Caixing Gu, Jaehui Park, Chase Peak, J. Rowley","doi":"10.4134/BKMS.B200437","DOIUrl":"https://doi.org/10.4134/BKMS.B200437","url":null,"abstract":"In this paper, we decompose (under unitary similarity) the Kronecker sum A A (= A⊗ I + I ⊗A) into a direct sum of irreducible matrices, when A is a 3×3 matrix. As a consequence we identify K(A A) as the direct sum of several full matrix algebras as predicted by Artin– Wedderburn theorem, where K(T ) is the unital algebra generated by T and T ∗.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"58 1","pages":"637-657"},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70363336","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}
. We study the solvability of the Fermat’s matrix equation in some classes of 2-by-2 matrices. We prove the Fermat’s matrix equation has infinitely many solutions in a set of 2-by-2 positive semidefinite integral matrices, and has no nontrivial solutions in some classes including 2-by-2 symmetric rational matrices and stochastic quadratic field matrices
{"title":"FERMAT'S EQUATION OVER 2-BY-2 MATRICES","authors":"M. Chien, Jie Meng","doi":"10.4134/BKMS.B200403","DOIUrl":"https://doi.org/10.4134/BKMS.B200403","url":null,"abstract":". We study the solvability of the Fermat’s matrix equation in some classes of 2-by-2 matrices. We prove the Fermat’s matrix equation has infinitely many solutions in a set of 2-by-2 positive semidefinite integral matrices, and has no nontrivial solutions in some classes including 2-by-2 symmetric rational matrices and stochastic quadratic field matrices","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"58 1","pages":"609-616"},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70363322","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":"INTEGRAL OPERATORS FROM MORREY TYPE SPACES TO WEIGHTED BMOA SPACES","authors":"R. Qian, Xiangling Zhu","doi":"10.4134/BKMS.B200464","DOIUrl":"https://doi.org/10.4134/BKMS.B200464","url":null,"abstract":"","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"14 1","pages":"815-828"},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70363757","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}
Denote by M+ the set of probability measures supported on R+. Suppose Vν is the variance function of the Cauchy-Stieltjes Kernel (CSK) family K−(ν) generated by a non degenerate probability measure ν ∈ M+. We determine the formula for variance function under boolean multiplicative convolution power. This formula is used to identify the relation between variance functions under the map ν 7→ Mt(ν) = ( ν (t+1) )∪× 1 t+1 from M+ onto itself.
{"title":"BOOLEAN MULTIPLICATIVE CONVOLUTION AND CAUCHY-STIELTJES KERNEL FAMILIES","authors":"Raouf Fakhfakh","doi":"10.4134/BKMS.B200380","DOIUrl":"https://doi.org/10.4134/BKMS.B200380","url":null,"abstract":"Denote by M+ the set of probability measures supported on R+. Suppose Vν is the variance function of the Cauchy-Stieltjes Kernel (CSK) family K−(ν) generated by a non degenerate probability measure ν ∈ M+. We determine the formula for variance function under boolean multiplicative convolution power. This formula is used to identify the relation between variance functions under the map ν 7→ Mt(ν) = ( ν (t+1) )∪× 1 t+1 from M+ onto itself.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"58 1","pages":"515-526"},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70363206","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}