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pro vyhledávání: '"Román, Pablo"'
There are several questions one may ask about polynomials $q_m(x)=q_m(x;t)=\sum_{n=0}^mt^mp_n(x)$ attached to a family of orthogonal polynomials $\{p_n(x)\}_{n\ge0}$. In this note we draw attention to the naturalness of this partial-sum deformation a
Externí odkaz:
http://arxiv.org/abs/2409.00261
We give an analog of exceptional polynomials in the matrix valued setting by considering suitable factorizations of a given second order differential operator and performing Darboux transformations. Orthogonality and density of the exceptional sequen
Externí odkaz:
http://arxiv.org/abs/2306.03223
Autor:
Gallo, Andrea L., Román, Pablo
We study algebras of differential and difference operators acting on matrix valued orthogonal polynomials (MVOPs) with respect to a weight matrix of the form $W^{(\nu)}_{\phi}(x) = x^{\nu}e^{-\phi(x)} W^{(\nu)}_{pol}(x)$, where $\nu>0$, $W^{(\nu)}_{p
Externí odkaz:
http://arxiv.org/abs/2303.06805
In this paper, we study parameter deformations of matrix valued orthogonal polynomials (MVOPs). These deformations are built on the use of certain matrix valued operators which are symmetric with respect to the matrix valued inner product defined by
Externí odkaz:
http://arxiv.org/abs/2302.14789
We analyze the large degree asymptotic behavior of matrix valued orthogonal polynomials (MVOPs), with a weight that consists of a Jacobi scalar factor and a matrix part. Using the Riemann-Hilbert formulation for MVOPs and the Deift-Zhou method of ste
Externí odkaz:
http://arxiv.org/abs/2210.00797
In this paper we introduce a notion of duality for matrix valued orthogonal polynomials with respect to a measure supported on the nonnegative integers. We show that the dual families are closely related to certain difference operators acting on the
Externí odkaz:
http://arxiv.org/abs/2110.13019
Autor:
Ruiz-González, Cristofer, Román, Pablo, Rueda-Ruzafa, Lola, Cardona, Diana, Requena, Mar, Alarcón, Raquel
Publikováno v:
In Psychiatry Research July 2024 337
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Using the theory introduced by Casper and Yakimov, we investigate the structure of algebras of differential and difference operators acting on matrix valued orthogonal polynomials (MVOPs) on $\mathbb{R}$, and we derive algebraic and differential rela
Externí odkaz:
http://arxiv.org/abs/1907.07447