Juan J. Moreno-Balcázar

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In this paper we consider a Sobolev inner product (f, g)S = ∫ fgdμ+ λ ∫ f ′g′dμ (1) and we characterize the measures μ for which there exists an algebraic relation between the polynomials, {Pn}, orthogonal with respect to the measure μ and the polynomials, {Qn}, orthogonal with respect to (1), such that the number of involved terms does not depend on the(More)
when :>0. In this way, the measure which appears in the first integral is not positive on [0, ) for + # R" [&1, 0]. The aim of this paper is the study of analytic properties of the polynomials Qn . First we give an explicit representation for Qn using an algebraic relation between Sobolev and Laguerre polynomials together with a recursive relation for k(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. 2000MSC: 42C05, 33C45.
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)
We say that the polynomial sequence (Q (λ) n ) is a semiclassical Sobolev polynomial sequence when it is orthogonal with respect to the inner product 〈p, r〉S = 〈u, p r〉+ λ 〈u,DpDr〉 , where u is a semiclassical linear functional, D is the differential, the difference or the q–difference operator, and λ is a positive constant. In this paper we get algebraic(More)
Inner products of the type 〈f, g〉S = 〈f, g〉ψ0 + 〈f ′, g〉ψ1, where one of the measures ψ0 or ψ1 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)