Artículo
Asymptotics of matrix valued orthogonal polynomials on [−1,1]
Fecha de publicación:
06/2023
Editorial:
Academic Press Inc Elsevier Science
Revista:
Advances in Mathematics
ISSN:
0001-8708
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We analyze the large degree asymptotic behavior of matrix valued orthogonal polynomials (MVOPs), with a weight that consists of a Jacobi scalar factor and a matrix part. Using the Riemann–Hilbert formulation for MVOPs and the Deift–Zhou method of steepest descent, we obtain asymptotic expansions for the MVOPs as the degree tends to infinity, in different regions of the complex plane (outside the interval of orthogonality, on the interval away from the endpoints and in neighborhoods of the endpoints), as well as for the matrix coefficients in the three-term recurrence relation for these MVOPs. The asymptotic analysis follows the work of Kuijlaars, McLaughlin, Van Assche and Vanlessen on scalar Jacobi-type orthogonal polynomials, but it also requires several different factorizations of the matrix part of the weight, in terms of eigenvalues/eigenvectors and using a matrix Szegő function. We illustrate the results with two main examples, MVOPs of Jacobi and Gegenbauer type, coming from group theory.
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Articulos(CIEM)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Citación
Deaño, Alfredo; Kuijlaars, Arno B. J.; Román, Pablo Manuel; Asymptotics of matrix valued orthogonal polynomials on [−1,1]; Academic Press Inc Elsevier Science; Advances in Mathematics; 423; 6-2023; 1-61
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