Geodesic
Markov's Theorem for Orthogonal Matrix Polynomials
Canadian journal of mathematics, Tome 48 (1996) no. 6, pp. 1180-1195

Voir la notice de l'article provenant de la source Cambridge University Press

Markov's Theorem shows asymptotic behavior of the ratio between the n-th orthonormal polynomial with respect to a positive measure and the n-th polynomial of the second kind. In this paper we extend Markov's Theorem for orthogonal matrix polynomials.
DOI : 10.4153/CJM-1996-062-4
Mots-clés : 42C05, 47A56, 65D32 
Duran, Antonio J. Markov's Theorem for Orthogonal Matrix Polynomials. Canadian journal of mathematics, Tome 48 (1996) no. 6, pp. 1180-1195. doi: 10.4153/CJM-1996-062-4
@article{10_4153_CJM_1996_062_4,
     author = {Duran, Antonio J.},
     title = {Markov's {Theorem} for {Orthogonal} {Matrix} {Polynomials}},
     journal = {Canadian journal of mathematics},
     pages = {1180--1195},
     year = {1996},
     volume = {48},
     number = {6},
     doi = {10.4153/CJM-1996-062-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-062-4/}
}
TY  - JOUR
AU  - Duran, Antonio J.
TI  - Markov's Theorem for Orthogonal Matrix Polynomials
JO  - Canadian journal of mathematics
PY  - 1996
SP  - 1180
EP  - 1195
VL  - 48
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-062-4/
DO  - 10.4153/CJM-1996-062-4
ID  - 10_4153_CJM_1996_062_4
ER  - 
%0 Journal Article
%A Duran, Antonio J.
%T Markov's Theorem for Orthogonal Matrix Polynomials
%J Canadian journal of mathematics
%D 1996
%P 1180-1195
%V 48
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-062-4/
%R 10.4153/CJM-1996-062-4
%F 10_4153_CJM_1996_062_4

[AN] [AN] Aptekarev, A. I. and Nikishin, E. M., The scattering problem for a discrete Sturm-Liouville operator, Mat. Sb. 121(1983), 327–358; Math. USSR-Sb. 49(1984), 325-355. Google Scholar

[B] [B] Berg, C., Markov's theorem revisited, J. Approx. Theory 78(1994), 260–275. Google Scholar

[D1] [D1] Duran, A. J., A generalization of Favards Theorem for polynomials satisfying a recurrence relation, J. Approx. Theory 74(1993), 83–109. Google Scholar

[D2] [D2] Duran, A. J., On orthogonal polynomials with respect to a positive definite matrix of measures, Canad. J. Math. 47(1995), 88–112. Google Scholar

[DL] [DL] Duran, A. J. and Lopez-Rodriguez, R., Orthogonal matrix polynomials: Zeros and Blumenthal's theorem, J. Approx. Theory 84(1996), 96–118. Google Scholar

[DV] [DV] Duran, A. J. and van Assche, W., Orthogonal matrix polynomials and higher order recurrence relations, Linear Algebra Appl. 219(1995), 261–280. Google Scholar

[G] [G] Gantmacher, F. R., The theory of matrices, Chelsea Publishing Company, New York, 1(1960). Google Scholar

[M] [M] Markov, A., Deux démonstrations de la convergence de certaines fractions continues, Acta Math. 19 (1895), 93–104. Google Scholar

[SV] [SV] Sinap, A. and van Assche, W., Polynomial interpolation and Gaussian quadrature for matrix valued function, Linear Algebra Appl. 207(1994), 71–114. Google Scholar

[S] [S] Stieltjes, T. J., Recherches sur les fractions continues, Ann. Fac. Sci. Toulouse Math. 8(1894), 1-22; [9] (1895), 5–47. Google Scholar

[Z] [Z] Zhani, D., Probleme des moments matriciels sur la droite: construction d'unefamille de solutions et questions d'unicite, Publications du Departement de Mathematiques, Universite Claude-Bernard-Lyon I, NouvelleserieD(1984), 1-84. Google Scholar

Cité par Sources :