Publicação: Szego type polynomials and para-orthogonal polynomials
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Academic Press Inc. Elsevier B.V.
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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 B.V. All rights reserved.
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Szegö polynomials, Para-orthogonal polynomials, Three term recurrence relation, Hypergeometric function
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Inglês
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Journal of Mathematical Analysis and Applications. San Diego: Academic Press Inc. Elsevier B.V., v. 370, n. 1, p. 30-41, 2010.
