| Texto completo | |
| Autor(es): |
Bracciali, Cleonice F.
;
Silva, Jairo S.
;
Ranga, A. Sri
;
Veronese, Daniel O.
Número total de Autores: 4
|
| Tipo de documento: | Artigo Científico |
| Fonte: | COMPUTATIONAL & APPLIED MATHEMATICS; v. 37, n. 2, p. 20-pg., 2018-05-01. |
| Resumo | |
It was shown recently that associated with a pair of real sequences {{c(n)}(n=1)(infinity), {d(n) }(n=1)(infinity)}, with {d(n) }(n=1)(infinity) a positive chain sequence, there exists a unique nontrivial probability measure mu on the unit circle. The Verblunsky coefficients {alpha(n) }(n=1)(infinity) associated with the orthogonal polynomials with respect to mu are given by the relation alpha(n-1) = (tau)over-bar(n-1) [1 - 2m(n) - ic(n)/1 - ic(n)], n >= 1, where tau(0) = 1, tau(n) = Pi(n)(k=1) (1 - ic(k))/(1 + ic(k)), n >= 1 and {m(n)}(n=0)(infinity) is the minimal parameter sequence of {d(n)}(n=1)(infinity). In this manuscript, we consider this relation and its consequences by imposing some restrictions of sign and periodicity on the sequences {c(n)}(n=1)(infinity) and {m(n)}(n=1)(infinity). When the sequence {c(n)}(n=1)(infinity) is of alternating sign, we use information about the zeros of associated para-orthogonal polynomials to show that there is a gap in the support of the measure in the neighbourhood of z = -1. Furthermore, we show that it is possible to generate periodic Verblunsky coefficients by choosing periodic sequences {c(n)}(n=1)(infinity) and {m(n)}(n=1)(infinity) with the additional restriction c(2n) = - c(2n-1), n >= 1. We also give some results on periodic Verblunsky coefficients from the point of view of positive chain sequences. An example is provided to illustrate the results obtained. (AU) | |
| Processo FAPESP: | 14/22571-2 - Polinômios ortogonais e seus similares com aplicações analíticas e numéricas |
| Beneficiário: | Cleonice Fátima Bracciali |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |