Pub Date : 2021-08-31DOI: 10.7146/math.scand.a-126021
S. Mukhigulashvili
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.
在本文中，我们研究了具有变元偏差的高阶微分方程组的可解性和唯一可解性问题 begin｛equipment*｝u_i^｛（m_i）｝q_{0i}（t），（i=overline{1，n}），text｛for$t in I$｝， end｛方程*｝在共轭$u_I^｛（j_1-1）｝（a）=a_｛ij_1}$，$u_I^{（j_2-1）}（b）=b_｛ij2}$，$j_1=overline｛1，k_I｝$，$j_2=overline{1，m_I-k_I}$，$I=overline{1，n｝$下，和右焦点$u_I^2｛（j-1-1）｝^｛（j2-1）｝（b）=b_｛ij2}$，$j_1=overline｛1，k_I｝$，$j2=overline{k_I+1，m_I}$，$I=overline{1，n｝$，边界条件，其中$u_{n+1｝=u1，L（i；R）中的$$ngeq2、$$m_igeq2和$$p_i是可测量函数，$F_i$是局部Caratheodory类运算符，并且$k_i$是数$m_i/2$的整数部分。本文得到了保证线性问题唯一可解性的有效充分条件，并明确考虑了自变量偏差的影响，在此基础上证明了非线性问题可解性和唯一可解的新条件。
{"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":" ","pages":""},"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}
Pub Date : 2021-08-31DOI: 10.7146/math.scand.a-126034
Ruifang Chen, Xianhe Zhao, Rui Li
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
{"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":" ","pages":""},"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}
Pub Date : 2021-08-31DOI: 10.7146/math.scand.a-126020
Rodrigo A. H. M. Cabral
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.
{"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":" ","pages":""},"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}
Pub Date : 2021-08-31DOI: 10.7146/math.scand.a-126053
N. Levenberg, F. Wielonsky
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 $mathbb{C}^2$.
{"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":" ","pages":""},"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}
Pub Date : 2021-08-31DOI: 10.7146/math.scand.a-126029
T. H. Freitas, V. H. Pérez, P. Lima
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 $nll0$.
{"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":" ","pages":""},"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}
Pub Date : 2021-08-31DOI: 10.7146/math.scand.a-126018
Kristin Courtney
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.
{"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":" ","pages":""},"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}
Pub Date : 2021-06-10DOI: 10.7146/math.scand.a-133257
L. Ihnatsyeva, Juha Lehrback, Antti V. Vahakangas
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.
{"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":" ","pages":""},"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}
Pub Date : 2021-04-30DOI: 10.7146/math.scand.a-133256
Rodrigo Cardeccia, Santiago Muro
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.
{"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":" ","pages":""},"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}
Pub Date : 2021-04-14DOI: 10.7146/math.scand.a-129686
E. Fricain, Camille Mau
In this paper, we introduce a general class of weighted spaces of holomorphic Dirichlet series (with real frequencies) analytic in some half-plane and study composition operators on these spaces. In the particular case when the symbol inducing the composition operator is an affine function, we give criteria for boundedness and compactness. We also study the cyclicity property and as a byproduct give a characterization so that the direct sum of the identity plus a weighted forward shift operator on $ell^2$ is cyclic.
{"title":"Weighted holomorphic Dirichlet series and composition operators with polynomial symbols","authors":"E. Fricain, Camille Mau","doi":"10.7146/math.scand.a-129686","DOIUrl":"https://doi.org/10.7146/math.scand.a-129686","url":null,"abstract":"In this paper, we introduce a general class of weighted spaces of holomorphic Dirichlet series (with real frequencies) analytic in some half-plane and study composition operators on these spaces. In the particular case when the symbol inducing the composition operator is an affine function, we give criteria for boundedness and compactness. We also study the cyclicity property and as a byproduct give a characterization so that the direct sum of the identity plus a weighted forward shift operator on $ell^2$ is cyclic.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42238536","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}
Pub Date : 2021-02-17DOI: 10.7146/MATH.SCAND.A-125054
Mathematica Scandinavica
Volume title pages
卷标题页
{"title":"Volume title pages","authors":"Mathematica Scandinavica","doi":"10.7146/MATH.SCAND.A-125054","DOIUrl":"https://doi.org/10.7146/MATH.SCAND.A-125054","url":null,"abstract":"Volume title pages","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":"127 1","pages":"1-4"},"PeriodicalIF":0.5,"publicationDate":"2021-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71076820","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}
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