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Boundaries for Gelfand transform images of Banach algebras of holomorphic functions 全纯函数Banach代数的Gelfand变换映象的边界
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2021-10-14 DOI: 10.7146/math.scand.a-134348
Y. Choi, Mingu Jung
{"title":"Boundaries for Gelfand transform images of Banach algebras of holomorphic functions","authors":"Y. Choi, Mingu Jung","doi":"10.7146/math.scand.a-134348","DOIUrl":"https://doi.org/10.7146/math.scand.a-134348","url":null,"abstract":"In this paper, we study boundaries for the Gelfand transform image of infinite dimensional analogues of the classical disk algebras. More precisely, given a certain Banach algebra $mathcal{A}$ of bounded holomorphic functions on the open unit ball $B_X$ of a complex Banach space $X$, we show that the Shilov boundary for the Gelfand transform image of $mathcal{A}$ can be explicitly described for a large class of Banach spaces. Some possible application of our result to the famous Corona theorem is also briefly discussed.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43029750","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}
引用次数: 0
The Fermat-Torricelli problem in the projective plane 投影平面上的Fermat-Torricelli问题
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2021-09-03 DOI: 10.7146/math.scand.a-133419
M. Tsakiris, Sihang Xu
{"title":"The Fermat-Torricelli problem in the projective plane","authors":"M. Tsakiris, Sihang Xu","doi":"10.7146/math.scand.a-133419","DOIUrl":"https://doi.org/10.7146/math.scand.a-133419","url":null,"abstract":"We pose and study the Fermat-Torricelli problem for a triangle in the projective plane under the sine distance. Our main finding is that if every side of the triangle has length greater than $sin 60^circ $, then the Fermat-Torricelli point is the vertex opposite the longest side. Our proof relies on a complete characterization of the equilateral case together with a deformation argument.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48032848","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}
引用次数: 0
Some two-point boundary value problems for systems of higher order functional differential equations 高阶泛函微分方程组的两点边值问题
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2021-08-31 DOI: 10.7146/math.scand.a-126021
S. Mukhigulashvili
{"title":"Some two-point boundary value problems for systems of higher order functional differential equations","authors":"S. Mukhigulashvili","doi":"10.7146/math.scand.a-126021","DOIUrl":"https://doi.org/10.7146/math.scand.a-126021","url":null,"abstract":"In the paper we study the question of the solvability and unique solvability of systems of the higher order differential equations with the argument deviations begin{equation*} u_i^{(m_i)}(t)=p_i(t)u_{i+1}(tau _{i}(t))+ q_i(t), (i=overline {1, n}), text {for $tin I:=[a, b]$}, end{equation*} and begin{equation*}u_i^{(m_i)} (t)=F_{i}(u)(t)+q_{0i}(t), (i = overline {1, n}), text {for $ tin I$}, end{equation*} under the conjugate $u_i^{(j_1-1)}(a)=a_{i j_1}$, $u_i^{(j_2-1)}(b)=b_{i j_2}$, $j_1=overline {1, k_i}$, $j_2=overline {1, m_i-k_i}$, $i=overline {1, n}$, and the right-focal $u_i^{(j_1-1)}(a)=a_{i j_1}$, $u_i^{(j_2-1)}(b)=b_{i j_2}$, $j_1=overline {1, k_i}$, $j_2=overline {k_i+1,m_i}$, $i=overline {1, n}$, boundary conditions, where $u_{n+1}=u_1, $ $ngeq 2, $ $m_igeq 2, $ $p_i in L_{infty }(I; R), $ $q_i, q_{0i}in L(I; R), $ $tau _icolon Ito I$ are the measurable functions, $F_i$ are the local Caratheodory's class operators, and $k_i$ is the integer part of the number $m_i/2$.In the paper are obtained the efficient sufficient conditions that guarantee the unique solvability of the linear problems and take into the account explicitly the effect of argument deviations, and on the basis of these results are proved new conditions of the solvability and unique solvability for the nonlinear problems.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48132281","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}
引用次数: 0
On $mathcal{M}$-normal embedded subgroups and the structure of finite groups $mathcal{M}$-正规嵌入子群与有限群的结构
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2021-08-31 DOI: 10.7146/math.scand.a-126034
Ruifang Chen, Xianhe Zhao, Rui Li
{"title":"On $mathcal{M}$-normal embedded subgroups and the structure of finite groups","authors":"Ruifang Chen, Xianhe Zhao, Rui Li","doi":"10.7146/math.scand.a-126034","DOIUrl":"https://doi.org/10.7146/math.scand.a-126034","url":null,"abstract":"Let $G$ be a group and $H$ be a subgroup of $G$. $H$ is said to be $mathcal{M}$-normal supplemented in $G$ if there exists a normal subgroup $K$ of $G$ such that $G=HK$ and $H_1K<G$ for every maximal subgroup $H_1$ of $H$. Furthermore, $H$ is said to be $mathcal{M}$-normal embedded in $G$ if there exists a normal subgroup $K$ of $G$ such that $G=HK$ and $Hcap K=1$ or $Hcap K$ is $mathcal{M}$-normal supplemented in $G$. In this paper, some new criteria for a group to be nilpotent and $p$-supersolvable for some prime $p$ are obtained.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42175000","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}
引用次数: 0
Strongly elliptic operators and exponentiation of operator Lie algebras 强椭圆算子与算子李代数的求幂
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2021-08-31 DOI: 10.7146/math.scand.a-126020
Rodrigo A. H. M. Cabral
{"title":"Strongly elliptic operators and exponentiation of operator Lie algebras","authors":"Rodrigo A. H. M. Cabral","doi":"10.7146/math.scand.a-126020","DOIUrl":"https://doi.org/10.7146/math.scand.a-126020","url":null,"abstract":"An intriguing feature which is often present in theorems regardingthe exponentiation of Lie algebras of unbounded linear operators onBanach spaces is the assumption of hypotheses on the Laplacianoperator associated with a basis of the operator Lie algebra.The main objective of this work is to show that one can substitutethe Laplacian by an arbitrary operator in the enveloping algebra andstill obtain exponentiation, as long as its closure generates astrongly continuous one-parameter semigroup satisfying certain normestimates, which are typical in the theory of strongly ellipticoperators.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45343860","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}
引用次数: 0
On transfinite diameters in $mathbb{C}^{d}$ for generalized notions of degree 关于广义度概念在$mathbb｛C｝^｛d｝$中的超限直径
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2021-08-31 DOI: 10.7146/math.scand.a-126053
N. Levenberg, F. Wielonsky
{"title":"On transfinite diameters in $mathbb{C}^{d}$ for generalized notions of degree","authors":"N. Levenberg, F. Wielonsky","doi":"10.7146/math.scand.a-126053","DOIUrl":"https://doi.org/10.7146/math.scand.a-126053","url":null,"abstract":"We give a general formula for the $C$-transfinite diameter $delta_C(K)$ of a compact set $Ksubset mathbb{C}^2$ which is a product of univariate compacta where $Csubset (mathbb{R}^+)^2$ is a convex body. Along the way we prove a Rumely type formula relating $delta_C(K)$ and the $C$-Robin function $rho_{V_{C,K}}$ of the $C$-extremal plurisubharmonic function $V_{C,K}$ for $C subset (mathbb{R}^+)^2$ a triangle $T_{a,b}$ with vertices $(0,0)$, $(b,0)$, $(0,a)$. Finally, we show how the definition of $delta_C(K)$ can be extended to include many nonconvex bodies $Csubset mathbb{R}^d$ for $d$-circled sets $Ksubset mathbb{C}^d$, and we prove an integral formula for $delta_C(K)$ which we use to compute a formula for $delta_C(mathbb{B})$ where $mathbb{B}$ is the Euclidean unit ball in $mathbb{C}^2$.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49393757","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}
引用次数: 0
Asymptotic behavior of $j$-multiplicities $j$-乘法的渐近性态
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2021-08-31 DOI: 10.7146/math.scand.a-126029
T. H. Freitas, V. H. Pérez, P. Lima
{"title":"Asymptotic behavior of $j$-multiplicities","authors":"T. H. Freitas, V. H. Pérez, P. Lima","doi":"10.7146/math.scand.a-126029","DOIUrl":"https://doi.org/10.7146/math.scand.a-126029","url":null,"abstract":"Let $R= oplus_{nin mathbb{N}_0}R_n$ be a Noetherian homogeneous ring with local base ring $(R_0,mathfrak{m}_0)$. Let $R_+= oplus_{nin mathbb{N}}R_n$ denote the irrelevant ideal of $R$ and let $M=oplus_{nin mathbb{Z}}M_n$ be a finitely generated graded $R$-module. When $dim(R_0)leq 2$ and $mathfrak{q}_0$ is an arbitrary ideal of $R_0$, we show that the $j$-multiplicity of the graded local cohomology module $j_0({mathfrak{q}_0},H_{R_+}^i(M)_n)$ has a polynomial behavior for all $nll0$.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49078135","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}
引用次数: 0
Universal $C^∗$-algebras with the local lifting property 具有局部提升性质的泛$C^ * $代数
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2021-08-31 DOI: 10.7146/math.scand.a-126018
Kristin Courtney
{"title":"Universal $C^∗$-algebras with the local lifting property","authors":"Kristin Courtney","doi":"10.7146/math.scand.a-126018","DOIUrl":"https://doi.org/10.7146/math.scand.a-126018","url":null,"abstract":"The Local Lifting Property (LLP) is a localized version of projectivity for completely positive maps between $mathrm{C}^*$-algebras. Outside of the nuclear case, very few $mathrm{C}^*$-algebras are known to have the LLP@. In this article, we show that the LLP holds for the algebraic contraction $mathrm{C}^*$-algebras introduced by Hadwin and further studied by Loring and Shulman. We also show that the universal Pythagorean $mathrm{C}^*$-algebras introduced by Brothier and Jones have the Lifting Property.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47570580","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}
引用次数: 7
Hardy-Sobolev inequalities and weighted capacities in metric spaces 度量空间中的Hardy-Sobolev不等式和加权容量
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2021-06-10 DOI: 10.7146/math.scand.a-133257
L. Ihnatsyeva, Juha Lehrback, Antti V. Vahakangas
{"title":"Hardy-Sobolev inequalities and weighted capacities in metric spaces","authors":"L. Ihnatsyeva, Juha Lehrback, Antti V. Vahakangas","doi":"10.7146/math.scand.a-133257","DOIUrl":"https://doi.org/10.7146/math.scand.a-133257","url":null,"abstract":"Let $Omega$ be an open set in a metric measure space $X$. Our main result gives an equivalence between the validity of a weighted Hardy–Sobolev inequality in $Omega$ and quasiadditivity of a weighted capacity with respect to Whitney covers of $Omega$. Important ingredients in the proof include the use of a discrete convolution as a capacity test function and a Maz'ya type characterization of weighted Hardy–Sobolev inequalities.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46727709","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}
引用次数: 0
Multiple recurrence and hypercyclicity 多重循环和超循环
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2021-04-30 DOI: 10.7146/math.scand.a-133256
Rodrigo Cardeccia, Santiago Muro
{"title":"Multiple recurrence and hypercyclicity","authors":"Rodrigo Cardeccia, Santiago Muro","doi":"10.7146/math.scand.a-133256","DOIUrl":"https://doi.org/10.7146/math.scand.a-133256","url":null,"abstract":"We study multiply recurrent and hypercyclic operators as a special case of $mathcal F$-hypercyclicity, where $mathcal F$ is the family of subsets of the natural numbers containing arbitrarily long arithmetic progressions. We prove several properties of hypercyclic multiply recurrent operators, we characterize those operators which are weakly mixing and multiply recurrent, and we show that there are operators that are multiply recurrent and hypercyclic but not weakly mixing.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46202734","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}
引用次数: 8
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