14 Result(s)
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Article
Open AccessSpectral transformations and second kind polynomials associated with a hermitian linear functional
The aim of this paper is to analyze the relation between the Christoffel transformations in the framework of hermitian linear functionals and the associated polynomials of the second kind through of their asso...
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Article
Discrete–Continuous Jacobi–Sobolev Spaces and Fourier Series
Let \(p\ge 1, \ell \in \mathbb {N}, \alpha ,\beta >-1\) p ≥ ...
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Article
Analytical Properties of Touchard-Based Hybrid Polynomials via Operational Techniques
In this paper, the Touchard-based Laguerre–Gould–Hopper polynomials are introduced by using operational techniques. We investigate many properties of such polynomials. In particular, generating functions, seri...
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Article
Linear Combinations of d-Orthogonal Polynomials
The regularity of a linear combination of r consecutive elements of a monic d-orthogonal polynomial sequence has been studied when $$(...
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Article
On Freud–Sobolev type orthogonal polynomials
In this contribution we deal with sequences of monic polynomials orthogonal with respect to the Freud Sobolev-type inner product $$\be...
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Article
Matrix Pearson Equations Satisfied by Koornwinder Weights in Two Variables
We consider Koornwinder’s method for constructing orthogonal polynomials in two variables from orthogonal polynomials in one variable. If semiclassical orthogonal polynomials in one variable are used, then Koo...
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Reference Work Entry In depth
Orthogonal Polynomials: Computation
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Article
Higher Order Coherent Pairs
In this paper, we study necessary and sufficient conditions for the relation $$\begin{array}{@{}l}P_n^{{[r]}}(x) + a_{n-1,r} P_{n-1}^...
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Article
Open AccessJacobi-Sobolev Orthogonal Polynomials: Asymptotics for N-Coherence of Measures
Let us introduce the Sobolev-type inner product , where and...
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Article
Open AccessA Cohen Type Inequality for Fourier Expansions of Orthogonal Polynomials with a Nondiscrete Jacobi-Sobolev Inner Product
Let denote the sequence of polynomials orthogonal with respect to the non-discrete Sobolev inner product
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Article
Asymptotic Properties of Orthogonal Polynomials with Respect to a Non-discrete Jacobi-Sobolev Inner Product
Let {Q n (α,β) (x)} n=0 ∞ denote the seque...
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Article
Asymptotics and Zeros of Sobolev Orthogonal Polynomials on Unbounded Supports
In this paper we present a survey about analytic properties of polynomials orthogonal with respect to a weighted Sobolev inner product such that the vector of measures has an unbounded support. In particular, ...
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Article
Discrete-Continuous Symmetrized Sobolev Inner Products
This paper deals with the bilinear symmetrization problem associated with Sobolev inner products. Let 007B;Q n } n=0 ∞ be the sequence of monic polynomials orthogonal with respe...
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Article
On a Modification of the Jacobi Linear Functional: Asymptotic Properties and Zeros of the Corresponding Orthogonal Polynomials
The paper deals with orthogonal polynomials in the case where the orthogonality condition is related to semiclassical functionals. The polynomials that we discuss are a generalization of Jacobi polynomials and...
