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Density Questions for the Truncated Matrix Moment Problem

Published online by Cambridge University Press:  20 November 2018

Antonio J. Duran  and
Pedro Lopez-Rodriguez
Antonio J. Duran
Affiliation:
Departamento de Análisis Matemático, Universidad de Sevilla, Apdo. 1160, 41080 Sevilla, Spain e-mail: [email protected], e-mail: [email protected], e-mail: [email protected]
Pedro Lopez-Rodriguez
Affiliation:
Departamento de Análisis Matemático, Universidad de Sevilla, Apdo. 1160, 41080 Sevilla, Spain e-mail: [email protected], e-mail: [email protected], e-mail: [email protected]
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Abstract

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For a truncated matrix moment problem, we describe in detail the set of positive definite matrices of measures μ in V2n (this is the set of solutions of the problem of degree 2n) for which the polynomials up to degree n are dense in the corresponding space L2(μ). These matrices of measures are exactly the extremal measures of the set Vn.

Keywords

42C054A60
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 4 , 01 August 1997 , pp. 708 - 721
Copyright
Copyright © Canadian Mathematical Society 1997

References

[A] Akhiezer, N.I., The classical moment problem and some related questions in analysis, English Translation, Oliver and Boyd, Edinburgh, 1965.Google Scholar
[AN] Aptekarev, A.I. and Nikishin, E.M., The scattering problem for a discrete Sturm-Liouville operator. Math. USSR-Sb. 49(1984), 325–355.Google Scholar
[D1] Durán, A.J., On orthogonal polynomials with respect to a positive definite matrix of measures, Canad. J. Math. 47(1995), 88–112.Google Scholar
[D2] Durán, A.J., Markov's Theorem for orthogonal matrix polynomials, Canad. J. Math. 48(1996), 1180–1195.Google Scholar
[DL1] Durán, A. J. and P. López-Rodríguez, , Orthogonal matrix polynomials: zeros and Blumenthal's Theorem,. J. Approx. Theory 84(1996), 96–118.Google Scholar
[DL2] Durán, A. J., The Lp space of a positive definite matrix of measures and density of matrix polynomials in L1, J. Approx. Theory, to appear.Google Scholar
[K] Kochubei, A.N., The extreme points of the set of solutions of the truncated matrix moment problem, Dopovıdı Akad. Nauk Ukräın. RSR Ser. A. (1972), 418–421.Google Scholar
[R] Rosenberg, M., The square-integrability of matrix-valued functions with respect to a non-negative hermitian. measure, Duke Math. J. 31(1964), 291–298.Google Scholar
[Z] Zhani, D., Problème des moments matriciels sur la droite: construction d’une famille de solutions et questions. d’unicité, Publ. Dept. Math., Université Claude-Bernard-Lyon I Nouvelle serie 21(1984), 1–84.Google Scholar