Matrix measures, moment spaces and Favard's theorem for the interval [0,1] and [0,∞)

By Holger Dette, W. J. Studden. 2002

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Abstract In this paper we study the moment spaces corresponding to matrix measures on compact intervals and on the nonnegative line [0,∞). A representation for nonnegative definite matrix polynomials is obtained, which is used to characterize moment points by properties of generalized Hankel matrices. We also derive an explicit representation of the orthogonal polynomials with respect to a given matrix measure, which generalizes the classical determinant representation of the one-dimensional case. Moreover, the coefficients in the recurrence relations can be expressed explicitly in terms of the moments of the matrix measure. These results are finally used to prove a refinement of the well-known Favard theorem for matrix measures, which characterizes the domain of the underlying measure of orthogonality by properties of the coefficients in the recurrence relationships.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2fd41e41b8a184feb2941f04c6e693e90b8e4396

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