Monotonicity and asymptotics of zeros of Sobolev type orthogonal polynomials: A general case

Castillo, Kenier; Mello, Mirela V. [UNESP]; Rafaeli, Fernando R. [UNESP]

Monotonicity and asymptotics of zeros of Sobolev type orthogonal polynomials: A general case

Data

2012-11-01

Autores

Castillo, Kenier

Mello, Mirela V.

Rafaeli, Fernando R.

Editor

Elsevier B.V.

Tipo

Artigo

Direito de acesso

Acesso restrito

Resumo

We investigate the location, monotonicity, and asymptotics of the zeros of the polynomials orthogonal with respect to the Sobolev type inner product< p, q > (lambda,c.j) = integral(b)(a) p(x)q(x)mu(x) + lambda p((j))(c)q((j))(c),where mu is a positive Borel measure, lambda >= 0, j is an element of Z(+), and c is not an element of (a, b). We prove that these zeros are monotonic function of the parameter A and establish their asymptotics when either lambda converges to zero or to infinity. The precise location of the extreme zeros is also analyzed. (c) 2012 IMACS. Published by Elsevier B.V. All rights reserved.