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

Abstract

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Distributions on matrix moment spaces

“…Throughout this paper we call the variables Z k (and similar quantities) canonical variables. Dette and Studden (2002) also showed the representation…”

“…The proof follows by similar arguments as in Dette and Studden (2002) and is therefore omitted. Note that the authors consider non-normalized measures, but the arguments can be extended to matrix probability measures.…”

“…If the support of a matrix measure Σ is a subset of [0, ∞), it follows by similar arguments as in Dette and Studden (2002) that there exists a sequence of matrices Z n ∈ R p×p , such that for n ≥ 1 the recursion coefficients in (2.17) of the monic matrix polynomials are given by…”

“…Dette and Nagel (2012a) considered distributions on moment spaces corresponding to scalar measures on the real line with an unbounded support. For matrix measures the corresponding moment of a matrix measure is given by a symmetric (hermitian) matrix and Dette and Studden (2002) obtained a characterization of the compact moment space corresponding to matrix measures on a compact interval. Dette and Nagel (2012b) used these results to investigate the asymptotic properties of random vectors with values in the moment space corresponding to matrix measures on the interval [0,1].…”

Relations between the orthogonal matrix polynomials on [a, b], Dyukarev-Stieltjes parameters, and Schur complements

“…Kovalishina [32], [33], Damanik/Pushnitski/Simon [18] and the references therein. See also [20], [21], [27], [19], [36], [26], [16], [17] and [8].…”