Orthogonal polynomials and analytic functions associated to positive definite matrices

For a positive definite infinite matrix A, we study the relationship between its associated sequence of orthonormal polynomials and the asymptotic behaviour of the smallest eigenvalue of its truncation An of size n X n. For the particular case of A being a Hankel or a Hankel block matrix, our result...

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Bibliographic Details
Authors: Berg, Christian, Durán Guardeño, Antonio José
Format: article
Status:Published version
Publication Date:2005
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/182564
Online Access:https://hdl.handle.net/11441/182564
https://doi.org/10.1016/j.jmaa.2005.09.093
Access Level:Open access
Keyword:Orthogonal polynomials
Index of determinacy
Orthogonal matrix polynomials
Description
Summary:For a positive definite infinite matrix A, we study the relationship between its associated sequence of orthonormal polynomials and the asymptotic behaviour of the smallest eigenvalue of its truncation An of size n X n. For the particular case of A being a Hankel or a Hankel block matrix, our results lead to a characterization of positive measures with finite index of determinacy and of completely indeterminate matrix moment problems, respectively.