R-II type recurrence, generalized eigenvalue problem and orthogonal polynomials on the unit circle

Autor(es)

Ismail, M. E. H. ^[1] ; Sri Ranga, A. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Cent Florida, Dept Math, Orlando, FL 32816 - USA

^[2] Univ Estadual Paulista, UNESP, IBILCE, DMAp, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Linear Algebra and its Applications; v. 562, p. 63-90, FEB 1 2018.
• Citações Web of Science: 3

Resumo

We consider a sequence of polynomials [P-n](n >= 0) satisfying a special RH type recurrence relation where the zeros of P-n are simple and lie on the real line. It turns out that the polynomial P-n, for any n >= 2, is the characteristic polynomial of a simple n x n generalized eigenvalue problem. It is shown that with this R-II type recurrence relation one can always associate a positive measure on the unit circle. The orthogonality property satisfied by P-n with respect to this measure is also obtained. Finally, examples are given to justify the results. (C) 2018 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 17/12324-6 - Polinômios ortogonais no círculo unitário e estudos relacionados
• Beneficiário: Alagacone Sri Ranga
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 16/09906-0 - Análise harmônica, teoria da aproximação, funções especiais e aplicações
• Beneficiário: Dimitar Kolev Dimitrov
• Modalidade de apoio: Auxílio à Pesquisa - Temático