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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Detalles Bibliográficos
Autores: Berg, Christian, Durán Guardeño, Antonio José
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2005
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/182564
Acceso en línea:https://hdl.handle.net/11441/182564
https://doi.org/10.1016/j.jmaa.2005.09.093
Access Level:acceso abierto
Palabra clave:Orthogonal polynomials
Index of determinacy
Orthogonal matrix polynomials
Descripción
Sumario: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.