Operator monotone functions, Jacobi operators and orthogonal polynomials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:401

Article

Uchiyama, Mitsuru

关键词: Orthogonal polynomials;    Lowner theorem;    Jacobi operator;    Pick function;    Nevanlinna function;   

DOI  :  10.1016/j.jmaa.2012.12.016

来源: Elsevier

【 摘 要 】

We reveal a connection between operator monotone functions and orthogonal polynomials. Especially, we express an operator monotone function with a Jacobi operator, and show that it is a limit of rational operator monotone functions. Further we prove that the 'principal inverse' of an orthogonal polynomial is operator monotone and hence it has a holomorphic extension to the open upper half plane, namely a Pick function (or Nevanlinna function). (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free