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Riesz's Theorem for Orthogonal Matrix Polynomials (1999)

López-Rodríguez, P.

Springer

Constructive approximation 15 (1999), S. 135-151

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ISSN: 1432-0940

Keywords: Key words. Orthogonal matrix polynomials, Matrix moment problem. AMS Classification. 42C05, 44A60.

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract. We describe the image through the Stieltjes transform of the set of solutions V of a matrix moment problem. We extend Riesz's theorem to the matrix setting, proving that those matrices of measures of V for which the matrix polynomials are dense in the corresponding $ {\cal L} $ 2 space are precisely those whose Stieltjes transform is an extremal point (in the sense of convexity) of the image set.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s003659900101

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