Francisco Marcellán

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math.CA2025

A class of Truncated Freud polynomials

Juan Carlos GarcÃa-Ardila, Francisco MarcellÃ¡n, Misael E. Marriaga

Consider the following truncated Freud linear functional $u_{z}$ depending on a parameter $z$ , $⟨ u_{z}, p ⟩ = \int_{0}^{\infty} p (x) e^{- z x^{4}} d x, z > 0.$ The…

math.CA2024

Symmetric Truncated Freud polynomials

Edmundo J. Huertas, Alberto Lastra, Francisco MarcellÃ¡n +1

We define the family of symmetric truncated Freud polynomials $P_{n} (x; z)$ , orthogonal with respect to the linear functional $u$ defined by \begin{equation*} \langle \mathbf…

math.CA2024

Dunkl symmetric coherent pairs of measures. An application to Fourier Dunkl-Sobolev expansions

Mabrouk Sghaier, Francisco MarcellÃ¡n

Let $T_{I^} ¼$ be the Dunkl operator. A pair of symmetric measures $(u, v)$ supported on a symmetric subset of the real line is said to be a symmetric Dunkl-coherent pair if…

math.CA2024

Recovering orthogonality from quasi-nature of Spectral transformations

Vikash Kumar, Francisco MarcellÃ¡n, A. Swaminathan

In this contribution, quasi-orthogonality of polynomials generated by Geronimus and Uvarov transformations is analyzed. An attempt is made to discuss the recovery of the source ort…

math.CA2024

Generalized Gauss-Rys orthogonal polynomials

Juan C. GarcÃa-Ardila, Francisco MarcellÃ¡n

Let $(P_{n} (x; z; I^»))_{n \geq 0}$ be the sequence of monic orthogonal polynomials with respect to the symmetric linear functional $s$ defined by $$\langle\mathbf{s},p\rangle=\…