On Orthogonal Polynomials With Respect to a Positive Definite Matrix of Measures

Antonio J. Duran

doi:10.4153/CJM-1995-005-8

Abstract

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In this paper, we prove that any sequence of polynomials (pn)n for which dgr(pn) = n which satisfies a (2N + l)-term recurrence relation is orthogonal with respect to a positive definite N × N matrix of measures. We use that result to prove asymptotic properties of the kernel polynomials associated to a positive measure or a positive definite matrix of measures. Finally, some examples are given.

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Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Berg, Christian and Duran, Antonio J. 1995. The index of determinacy for measures and the 𝑙²-norm of orthonormal polynomials. Transactions of the American Mathematical Society, Vol. 347, Issue. 8, p. 2795.

Durán, A.J. and Van Assche, W. 1995. Orthogonal matrix polynomials and higher-order recurrence relations. Linear Algebra and its Applications, Vol. 219, Issue. , p. 261.

Duran, Antonio J. 1996. Markov's Theorem for Orthogonal Matrix Polynomials. Canadian Journal of Mathematics, Vol. 48, Issue. 6, p. 1180.

Duran, Antonio J. 1997. Matrix Inner Product Having a Matrix Symmetric Second Order Differential Operator. Rocky Mountain Journal of Mathematics, Vol. 27, Issue. 2,

Duran, Antonio J. and Lopez-Rodriguez, Pedro 1997. The LpSpace of a Positive Definite Matrix of Measures and Density of Matrix Polynomials inL1. Journal of Approximation Theory, Vol. 90, Issue. 2, p. 299.

Jódar, L. Navarro, E. and Defez, E. 1997. On the best approximation matrix problem and matrix Fourier series. Approximation Theory and its Applications, Vol. 13, Issue. 4, p. 88.

Jódar, Lucas and Defez, Emilio 1998. On Hermite matrix polynomials and Hermite matrix functions. Approximation Theory and its Applications, Vol. 14, Issue. 1, p. 36.

Duran, Antonio J. 1999. Ratio Asymptotics for Orthogonal Matrix Polynomials. Journal of Approximation Theory, Vol. 100, Issue. 2, p. 304.

Duran, A. J. Lopez-Rodriguez, P. and Saff, E. B. 1999. Zero asymptotic behaviour for orthogonal matrix polynomials. Journal d'Analyse Mathématique, Vol. 78, Issue. 1, p. 37.

Emilio, Defez and Lucas, Jódar 2000. On the best approximation matrix problem for integrable matrix functions. Approximation Theory and its Applications, Vol. 16, Issue. 3, p. 56.

Duran, Antonio J. and Lopez-Rodriguez, Pedro 2000. N-Extremal Matrices of Measures for an Indeterminate Matrix Moment Problem. Journal of Functional Analysis, Vol. 174, Issue. 2, p. 301.

Szafraniec, Franciszek Hugon 2001. On matrix integration of matrix polynomials. Journal of Computational and Applied Mathematics, Vol. 133, Issue. 1-2, p. 611.

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Duran, Antonio J and Daneri-Vias, Enrique 2001. Ratio Asymptotics for Orthogonal Matrix Polynomials with Unbounded Recurrence Coefficients. Journal of Approximation Theory, Vol. 110, Issue. 1, p. 1.

Duran, A.J. and Saff, E.B. 2001. Zero Location for Nonstandard Orthogonal Polynomials. Journal of Approximation Theory, Vol. 113, Issue. 1, p. 127.

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Dette, Holger and Studden, William J. 2002. A note on the matrix valued q-d algorithm and matrix orthogonal polynomials on [0,1] and [0,∞). Journal of Computational and Applied Mathematics, Vol. 148, Issue. 2, p. 349.

Dette, Holger and Studden, William J. 2002. Matrix measures, moment spaces and Favard's theorem for the interval [0,1] and [0,∞). Linear Algebra and its Applications, Vol. 345, Issue. 1-3, p. 169.

Duran, Antonio J. and Daneri, Enrique 2002. Weak convergence for orthogonal matrix polynomials. Indagationes Mathematicae, Vol. 13, Issue. 1, p. 47.

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Article contents

On Orthogonal Polynomials With Respect to a Positive Definite Matrix of Measures

Abstract

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References

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

On Orthogonal Polynomials With Respect to a Positive Definite Matrix of Measures

Abstract

Keywords

References

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