Weighted shift operators, orthogonal polynomials and chain sequences

被引：0
作者：
Rupert Lasser
Josef Obermaier
机构：
[1] Munich University of Technology,
[2] Centre of Mathematics,undefined
[3] Helmholtz Zentrum München,undefined
[4] German Research Center for Environmental Health,undefined
[5] Scientific Computing Research Unit,undefined
来源：
Acta Scientiarum Mathematicarum | 2020年 / 86卷
关键词：
47B36; 47B37; 33C45; weighted shift operators; Jacobi operators; chain sequences; orthogonal polynomials;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The main purpose of this paper is to use chain sequences to study spectral properties of weighted shift operators A and of tridiagonal operators Re A. Characterizations of chain sequences and relations to Haar sequences are derived. We use these results to compare the spectral radius, the numerical radius and the norm of A and Re A. As an example we study orthogonal polynomials defined by a recursion formula with almost constant coefficients.
引用
收藏
页码：331 / 342
页数：11
相关论文
共 13 条
  • [1] Berger C A(1967)Mapping theorems for the numerical range Amer. J. Math. 89 1047-1055
  • [2] Stampfli J G(1980)Spectral properties of real parts of weighted shift operators Indiana Univ. Math. J. 29 249-259
  • [3] Dombrowski J(1986)Orthogonal polynomials, measures and recurrence relations SIAM J. Math. Anal. 17 752-759
  • [4] Dombrowski J(1930)On a set of polynomials Ann. Math. 31 681-686
  • [5] Nevai P(1994)Orthogonal polynomials and hypergroups II–the symmetric case Trans. Amer. Math. Soc. 341 749-770
  • [6] Geronimus J(1970)Approximate point spectrum of a weighted shift Trans. Amer. Math. Soc. 147 349-356
  • [7] Lasser R(1974)Weighted shift operators and analytic function theory Math. Surveys 13 49-128
  • [8] Ridge W C(1983)The numerical range of a weighted shift Proc. Amer. Math. Soc. 88 495-502
  • [9] Shields A(1998)Chain sequences, orthogonal polynomials, and Jacobi matrices J. Approx. Theory 92 59-73
  • [10] Stout Q F(2011)Numerical ranges of weighted shifts J. Math. Anal. Appl. 381 897-909
12