ORTHOGONAL POLYNOMIALS WITH RESPECT TO A FAMILY OF SOBOLEV INNER PRODUCTS ON THE UNIT CIRCLE

Autor(es)

Ranga, A. Sri

• Tipo de documento: Artigo Científico
• Fonte: Proceedings of the American Mathematical Society; v. 144, n. 3, p. 1129-1143, MAR 2016.
• Citações Web of Science: 1

Resumo

The principal objective here is to look at some algebraic properties of the orthogonal polynomials Psi((b,s,t))(n) with respect to the Sobolev inner product on the unit circle < f, g >(S(b,s,t)) = (1 - t) < f, g >(mu(b)) + t <(f(1))over bar> g(1) + s < f', g'>(mu(b+1)) where < f, g >(mu(b)) - tau(b)/2 pi integral(2 pi)(0) f(e(i theta))g(e(i theta)) (e(pi-theta))(Im(b)) (sin(2)(theta/2))(Re(b))d theta. Here, Re(b) > -1/2, 0 <= t < 1, s > 0 and tau(b) is taken to be such that < 1, 1 >(mu(b)) = 1. We show that, for example, the monic Sobolev orthogonal polynomials. Psi n((b,s,t)) satisfy the recurrence Psi n((b,s,t)) (z)-beta n((b,s,t)) Psi((b,s,t))(n-1) (z) = Phi((b,s,t))(n) (z) n >= 1, where Psi((b,s,t))(n) are the monic orthogonal polynomials with respect to the inner product < f, g >(S(b,s,t)) = (1 - t) < f, g >(mu(b)) + t <(f(1))over bar> g(1). Some related bounds and asymptotic properties are also given. (AU)

• Processo FAPESP: 09/13832-9 - Polinômios ortogonais, funções especiais e aplicações
• Beneficiário: Dimitar Kolev Dimitrov
• Linha de fomento: Auxílio à Pesquisa - Temático