Pub Date : 2014-03-01DOI: 10.2478/s11533-013-0348-z
A. B. D. Monvel, Lech Zielinski
We consider an infinite Jacobi matrix with off-diagonal entries dominated by the diagonal entries going to infinity. The corresponding self-adjoint operator J has discrete spectrum and our purpose is to present results on the approximation of eigenvalues of J by eigenvalues of its finite submatrices.
{"title":"Approximation of eigenvalues for unbounded Jacobi matrices using finite submatrices","authors":"A. B. D. Monvel, Lech Zielinski","doi":"10.2478/s11533-013-0348-z","DOIUrl":"https://doi.org/10.2478/s11533-013-0348-z","url":null,"abstract":"We consider an infinite Jacobi matrix with off-diagonal entries dominated by the diagonal entries going to infinity. The corresponding self-adjoint operator J has discrete spectrum and our purpose is to present results on the approximation of eigenvalues of J by eigenvalues of its finite submatrices.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"94 1","pages":"445-463"},"PeriodicalIF":0.0,"publicationDate":"2014-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74242792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-03-01DOI: 10.2478/s11533-013-0358-x
M. Popov, E. Semenov, D. O. Vatsek
It is known that if a rearrangement invariant (r.i.) space E on [0, 1] has an unconditional basis then every linear bounded operator on E is a sum of two narrow operators. On the other hand, for the classical space E = L1[0, 1] having no unconditional basis the sum of two narrow operators is a narrow operator. We show that a Köthe space on [0, 1] having “lots” of nonnarrow operators that are sum of two narrow operators need not have an unconditional basis. However, we do not know if such an r.i. space exists. Another result establishes sufficient conditions on an r.i. space E under which the orthogonal projection onto the closed linear span of the Rademacher system is a hereditarily narrow operator. This, in particular, answers a question of the first named author and Randrianantoanina (Problem 11.9 in [Popov M., Randrianantoanina B., Narrow Operators on Function Spaces and Vector Lattices, de Gruyter Stud. Math., 45, Walter de Gruyter, Berlin, 2013]).
已知，如果重排不变空间E在[0,1]上具有无条件基，则E上的每一个线性有界算子都是两个窄算子的和。另一方面，对于没有无条件基的经典空间E = L1[0,1]，两个窄算子的和是一个窄算子。我们证明了在[0,1]上的Köthe空间具有“许多”非窄算子，这些非窄算子是两个窄算子的和，不需要有无条件基。然而，我们不知道这样的r.i.空间是否存在。另一个结果建立了在r.i.空间E上Rademacher系统在闭线性张成空间上的正交投影是一个遗传窄算子的充分条件。这特别地回答了第一位作者和Randrianantoanina(问题11.9)在[Popov M.， Randrianantoanina B.，函数空间和向量格上的窄算子，de Gruyter Stud]中的问题。数学。， 45, Walter de Gruyter，柏林，2013])。
{"title":"Some problems on narrow operators on function spaces","authors":"M. Popov, E. Semenov, D. O. Vatsek","doi":"10.2478/s11533-013-0358-x","DOIUrl":"https://doi.org/10.2478/s11533-013-0358-x","url":null,"abstract":"It is known that if a rearrangement invariant (r.i.) space E on [0, 1] has an unconditional basis then every linear bounded operator on E is a sum of two narrow operators. On the other hand, for the classical space E = L1[0, 1] having no unconditional basis the sum of two narrow operators is a narrow operator. We show that a Köthe space on [0, 1] having “lots” of nonnarrow operators that are sum of two narrow operators need not have an unconditional basis. However, we do not know if such an r.i. space exists. Another result establishes sufficient conditions on an r.i. space E under which the orthogonal projection onto the closed linear span of the Rademacher system is a hereditarily narrow operator. This, in particular, answers a question of the first named author and Randrianantoanina (Problem 11.9 in [Popov M., Randrianantoanina B., Narrow Operators on Function Spaces and Vector Lattices, de Gruyter Stud. Math., 45, Walter de Gruyter, Berlin, 2013]).","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"70 1","pages":"476-482"},"PeriodicalIF":0.0,"publicationDate":"2014-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81554294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-03-01DOI: 10.2478/s11533-013-0355-0
M. J. Evans
Let Fn denote the free group of rank n and d(G) the minimal number of generators of the finitely generated group G. Suppose that R ↪ Fm ↠ G and S ↪ Fm ↠ G are presentations of G and let $$bar R$$ and $$bar S$$ denote the associated relation modules of G. It is well known that $$bar R oplus (mathbb{Z}G)^{d(G)} cong bar S oplus (mathbb{Z}G)^{d(G)}$$ even though it is quite possible that . However, to the best of the author’s knowledge no examples have appeared in the literature with the property that . Our purpose here is to exhibit, for each integer k ≥ 1, a group G that has presentations as above such that . Our approach depends on the existence of nonfree stably free modules over certain commutative rings and, in particular, on the existence of certain Hurwitz-Radon systems of matrices with integer entries discovered by Geramita and Pullman. This approach was motivated by results of Adams concerning the number of orthonormal (continuous) vector fields on spheres.
设Fn表示秩为n的自由群，d(G)表示有限生成群G的最小生成子数。设R“f > Fm > G”和S“f > Fm > G”是G和Let的表示 $$bar R$$ 和 $$bar S$$ 表示g的关联关系模块，众所周知 $$bar R oplus (mathbb{Z}G)^{d(G)} cong bar S oplus (mathbb{Z}G)^{d(G)}$$ 尽管很有可能。然而，据作者所知，没有例子出现在文献与属性。我们这里的目的是展示，对于每一个整数k≥1，群G具有如上的表示，如下:我们的方法依赖于某些交换环上的非自由稳定自由模的存在性，特别是依赖于Geramita和Pullman发现的某些整数项矩阵的Hurwitz-Radon系统的存在性。这种方法的动机是亚当斯关于球面上的标准正交(连续)向量场的数量的结果。
{"title":"Relation modules of infinite groups, II","authors":"M. J. Evans","doi":"10.2478/s11533-013-0355-0","DOIUrl":"https://doi.org/10.2478/s11533-013-0355-0","url":null,"abstract":"Let Fn denote the free group of rank n and d(G) the minimal number of generators of the finitely generated group G. Suppose that R ↪ Fm ↠ G and S ↪ Fm ↠ G are presentations of G and let $$bar R$$ and $$bar S$$ denote the associated relation modules of G. It is well known that $$bar R oplus (mathbb{Z}G)^{d(G)} cong bar S oplus (mathbb{Z}G)^{d(G)}$$ even though it is quite possible that . However, to the best of the author’s knowledge no examples have appeared in the literature with the property that . Our purpose here is to exhibit, for each integer k ≥ 1, a group G that has presentations as above such that . Our approach depends on the existence of nonfree stably free modules over certain commutative rings and, in particular, on the existence of certain Hurwitz-Radon systems of matrices with integer entries discovered by Geramita and Pullman. This approach was motivated by results of Adams concerning the number of orthonormal (continuous) vector fields on spheres.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"51 1","pages":"436-444"},"PeriodicalIF":0.0,"publicationDate":"2014-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90296384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-03-01DOI: 10.2478/s11533-013-0352-3
V. Yurko
We study inverse spectral problems for ordinary differential equations on compact star-type graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function (m-function) for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.
{"title":"Inverse problems on star-type graphs: differential operators of different orders on different edges","authors":"V. Yurko","doi":"10.2478/s11533-013-0352-3","DOIUrl":"https://doi.org/10.2478/s11533-013-0352-3","url":null,"abstract":"We study inverse spectral problems for ordinary differential equations on compact star-type graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function (m-function) for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"26 1","pages":"483-499"},"PeriodicalIF":0.0,"publicationDate":"2014-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87487360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-02-20DOI: 10.2478/s11533-013-0383-9
Lenka Zalabová
We construct a non-homogeneous contact projective structure which is symmetric from the point of view of parabolic geometries.
从抛物线几何的观点出发，构造了一个对称的非齐次接触投影结构。
{"title":"A non-homogeneous, symmetric contact projective structure","authors":"Lenka Zalabová","doi":"10.2478/s11533-013-0383-9","DOIUrl":"https://doi.org/10.2478/s11533-013-0383-9","url":null,"abstract":"We construct a non-homogeneous contact projective structure which is symmetric from the point of view of parabolic geometries.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"362 1","pages":"879-886"},"PeriodicalIF":0.0,"publicationDate":"2014-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75094077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-02-20DOI: 10.2478/s11533-013-0385-7
Z. Pogorzały
In this note we show that there are a lot of orbit algebras that are invariant under stable equivalences of Morita type between self-injective algebras. There are also indicated some links between Auslander-Reiten periodicity of bimodules and noetherianity of their orbit algebras.
{"title":"Orbit algebras that are invariant under stable equivalences of Morita type","authors":"Z. Pogorzały","doi":"10.2478/s11533-013-0385-7","DOIUrl":"https://doi.org/10.2478/s11533-013-0385-7","url":null,"abstract":"In this note we show that there are a lot of orbit algebras that are invariant under stable equivalences of Morita type between self-injective algebras. There are also indicated some links between Auslander-Reiten periodicity of bimodules and noetherianity of their orbit algebras.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"217 1","pages":"813-823"},"PeriodicalIF":0.0,"publicationDate":"2014-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75778512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-02-15DOI: 10.2478/s11533-013-0380-z
O. Katkova, A. Vishnyakova
Let be the cone of real univariate polynomials of degree ≤ 2n which are nonnegative on the real axis and have nonnegative coefficients. We describe the extremal rays of this convex cone and the class of linear operators, acting diagonally in the standard monomial basis, preserving this cone.
{"title":"The cone of nonnegative polynomials with nonnegative coefficients and linear operators preserving this cone","authors":"O. Katkova, A. Vishnyakova","doi":"10.2478/s11533-013-0380-z","DOIUrl":"https://doi.org/10.2478/s11533-013-0380-z","url":null,"abstract":"Let be the cone of real univariate polynomials of degree ≤ 2n which are nonnegative on the real axis and have nonnegative coefficients. We describe the extremal rays of this convex cone and the class of linear operators, acting diagonally in the standard monomial basis, preserving this cone.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"11 1","pages":"752-760"},"PeriodicalIF":0.0,"publicationDate":"2014-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89533470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-02-15DOI: 10.2478/s11533-013-0375-9
Y. Davydov, V. Paulauskas
We consider a centered Gaussian random field X = {Xt : t ∈ T} with values in a Banach space $$mathbb{B}$$ defined on a parametric set T equal to ℝm or ℤm. It is supposed that the distribution of Xt is independent of t. We consider the asymptotic behavior of closed convex hulls Wn = conv{Xt : t ∈ Tn}, where (Tn) is an increasing sequence of subsets of T. We show that under some conditions of weak dependence for the random field under consideration and some sequence (bn)n≥1 with probability 1, (in the sense of Hausdorff distance), where the limit set is the concentration ellipsoid of . The asymptotic behavior of the mathematical expectations Ef(Wn), where f is some function, is also studied.
{"title":"On the asymptotic form of convex hulls of Gaussian random fields","authors":"Y. Davydov, V. Paulauskas","doi":"10.2478/s11533-013-0375-9","DOIUrl":"https://doi.org/10.2478/s11533-013-0375-9","url":null,"abstract":"We consider a centered Gaussian random field X = {Xt : t ∈ T} with values in a Banach space $$mathbb{B}$$ defined on a parametric set T equal to ℝm or ℤm. It is supposed that the distribution of Xt is independent of t. We consider the asymptotic behavior of closed convex hulls Wn = conv{Xt : t ∈ Tn}, where (Tn) is an increasing sequence of subsets of T. We show that under some conditions of weak dependence for the random field under consideration and some sequence (bn)n≥1 with probability 1, (in the sense of Hausdorff distance), where the limit set is the concentration ellipsoid of . The asymptotic behavior of the mathematical expectations Ef(Wn), where f is some function, is also studied.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"20 1","pages":"711-720"},"PeriodicalIF":0.0,"publicationDate":"2014-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81165868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-02-15DOI: 10.2478/s11533-013-0377-7
K. Izuchi, Y. Izuchi, S. Ohno
Associated with some properties of weighted composition operators on the spaces of bounded harmonic and analytic functions on the open unit disk $$mathbb{D}$$, we obtain conditions in terms of behavior of weight functions and analytic self-maps on the interior $$mathbb{D}$$ and on the boundary $$partial mathbb{D}$$ respectively. We give direct proofs of the equivalence of these interior and boundary conditions. Furthermore we give another proof of the estimate for the essential norm of the difference of weighted composition operators.
{"title":"Boundary vs. interior conditions associated with weighted composition operators","authors":"K. Izuchi, Y. Izuchi, S. Ohno","doi":"10.2478/s11533-013-0377-7","DOIUrl":"https://doi.org/10.2478/s11533-013-0377-7","url":null,"abstract":"Associated with some properties of weighted composition operators on the spaces of bounded harmonic and analytic functions on the open unit disk $$mathbb{D}$$, we obtain conditions in terms of behavior of weight functions and analytic self-maps on the interior $$mathbb{D}$$ and on the boundary $$partial mathbb{D}$$ respectively. We give direct proofs of the equivalence of these interior and boundary conditions. Furthermore we give another proof of the estimate for the essential norm of the difference of weighted composition operators.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"46 1","pages":"761-777"},"PeriodicalIF":0.0,"publicationDate":"2014-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80463874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-02-13DOI: 10.2478/s11533-013-0381-y
Jinrong Wang, Yong Zhou, Michal Feckan
In this paper, we develop the approach and techniques of [Boucherif A., Precup R., Semilinear evolution equations with nonlocal initial conditions, Dynam. Systems Appl., 2007, 16(3), 507–516], [Zhou Y., Jiao F., Nonlocal Cauchy problem for fractional evolution equations, Nonlinar Anal. Real World Appl., 2010, 11(5), 4465–4475] to deal with nonlocal Cauchy problem for semilinear fractional order evolution equations. We present two new sufficient conditions on existence of mild solutions. The first result relies on a growth condition on the whole time interval via Schaefer fixed point theorem. The second result relies on a growth condition splitted into two parts, one for the subinterval containing the points associated with the nonlocal conditions, and the other for the rest of the interval via O’Regan fixed point theorem.
{"title":"On the nonlocal Cauchy problem for semilinear fractional order evolution equations","authors":"Jinrong Wang, Yong Zhou, Michal Feckan","doi":"10.2478/s11533-013-0381-y","DOIUrl":"https://doi.org/10.2478/s11533-013-0381-y","url":null,"abstract":"In this paper, we develop the approach and techniques of [Boucherif A., Precup R., Semilinear evolution equations with nonlocal initial conditions, Dynam. Systems Appl., 2007, 16(3), 507–516], [Zhou Y., Jiao F., Nonlocal Cauchy problem for fractional evolution equations, Nonlinar Anal. Real World Appl., 2010, 11(5), 4465–4475] to deal with nonlocal Cauchy problem for semilinear fractional order evolution equations. We present two new sufficient conditions on existence of mild solutions. The first result relies on a growth condition on the whole time interval via Schaefer fixed point theorem. The second result relies on a growth condition splitted into two parts, one for the subinterval containing the points associated with the nonlocal conditions, and the other for the rest of the interval via O’Regan fixed point theorem.","PeriodicalId":50988,"journal":{"name":"Central European Journal of Mathematics","volume":"21 1","pages":"911-922"},"PeriodicalIF":0.0,"publicationDate":"2014-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82543820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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