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...
| Authors: | , |
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| 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 |
| 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. |
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