Orthogonal polynomials and analytic functions associated to positive definite matrices |
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Authors: | Christian Berg,Antonio J. Durá n |
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Affiliation: | a Matematisk Institut, Københavns Universitet, Universitetsparken 5, DK-2100 København Ø, Denmark b Departamento de Análisis Matemático, Universidad de Sevilla, PO BOX 1160, E-41080 Sevilla, Spain |
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Abstract: | 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×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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Keywords: | Orthogonal polynomials Index of determinacy Orthogonal matrix polynomials |
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