Juan J. Moreno-Balcázar

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In this paper we consider a Sobolev inner product (f, g) S = f gdµ + λ f g dµ (1) and we characterize the measures µ for which there exists an algebraic relation between the polynomials, {P n }, orthogonal with respect to the measure µ and the polynomials, {Q n }, orthogonal with respect to (1), such that the number of involved terms does not depend on the(More)
We consider a generalization of the classical Hermite polynomials by the addition of terms involving derivatives in the inner product. This type of generalization has been studied in the literature from the point of view of the algebraic properties. Thus, our aim is to study the asymptotics of this sequence of nonstandard orthogonal polynomials. In fact, we(More)
This paper deals with Mehler-Heine type asymptotic formulas for so called discrete Sobolev orthogonal polynomials whose continuous part is given by Laguerre and generalized Hermite measures. We use a new approach which allows to solve the problem when the discrete part contains an arbitrary (finite) number of mass points.
Inner products of the type f, g S = f, g ψ 0 + f , g ψ 1 , where one of the measures ψ 0 or ψ 1 is the measure associated with the Jacobi polynomials, are usually referred to as Jacobi-Sobolev inner products. This paper deals with some asymptotic relations for the orthogonal polynomials with respect to a class of Jacobi-Sobolev inner products. The inner(More)