Szego type polynomials and para-orthogonal polynomials

Autor(es)

Lamblem, R. L. ^[1] ; McCabe, J. H. ^[2] ; Pinar, M. A. ^[3] ; Ranga, A. Sri ^[1]

Afiliação do(s) autor(es)

^[1] UNESP Univ Estadual Paulista, IBILCE, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

^[2] Univ St Andrews, Sch Math, Dept Appl Math, St Andrews KY16 9AJ, Fife - Scotland

^[3] Univ Granada, Dept Matemat Aplicada, E-18071 Granada - Spain

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 370, n. 1, p. 30-41, OCT 1 2010.
• Citações Web of Science: 4

Resumo

Szego type polynomials with respect to a linear functional M for which the moments M{[}t(n)] = mu(-n) are all complex, mu(-n) = mu(n) and D(n) not equal 0 for n >= 0. are considered. Here, D(n) are the associated Toeplitz determinants. Para-orthogonal polynomials are also studied without relying on any integral representation. Relation between the Toeplitz determinants of two different types of moment functionals are given. Starting from the existence of polynomials similar to para-orthogonal polynomials, sufficient conditions for the existence of Szego type polynomials are also given. Examples are provided to justify the results. (C) 2010 Elsevier Inc. All rights reserved. (AU)