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Juan EF Díaz

Publications and source records attributed to Juan EF Díaz.

5 recordsLinked to original sources
arXiv2024

Bidiagonal factorization of recurrence banded matrices in mixed multiple orthogonality

This paper demonstrates how to explicitly construct a bidiagonal factorization of the banded recurrence matrix that appears in mixed multiple orthogonality on the step-line in terms of the coeffcients of the mixed multiple orthogonal polynomials. The construction is based on the \(LU\) factorization of the moment matrix and Christoffel transformations applied to the matrix of measures and the associated mixed multiple orthogonal polynomials.

math.CA↗
arXiv2024

Integral and hypergeometric representations for multiple orthogonal polynomials

This paper addresses two primary objectives in the realm of classical multiple orthogonal polynomials with an arbitrary number of weights. Firstly, it establishes new and explicit hypergeometric expressions for type I Hahn multiple orthogonal polynomials. Secondly, applying the residue theorem and the Mellin transform, the paper derives contour integral representations for several families of orthogonal polynomials. Specifically, it presents contour integral formulas for both type I and type II multiple orthogonal polynomials in the Laguerre of the first kind, Jacobi-Piñeiro, and Hahn families. The evaluation of these integrals leads to explicit hypergeometric representations.

math.CA↗
arXiv2024

Finite Markov chains and multiple orthogonal polynomials

This paper investigates stochastic finite matrices and the corresponding finite Markov chains constructed using recurrence matrices for general families of orthogonal polynomials and multiple orthogonal polynomials. The paper explores the spectral theory of transition matrices, utilizing both orthogonal and multiple orthogonal polynomials. Several properties are derived, including classes, periodicity, recurrence, stationary states, ergodicity, expected recurrence times, time-reversed chains, and reversibility. Furthermore, the paper uncovers factorization in terms of pure birth and pure death processes. The case study focuses on hypergeometric orthogonal polynomials, where all the computations can be carried out effectively. Particularly within the Askey scheme, all descendants under Hahn (excluding Bessel), such as Hahn, Jacobi, Meixner, Kravchuk, Laguerre, Charlier, and Hermite, present interesting examples of recurrent reversible birth and death finite Markov chains. Additionally, the paper considers multiple orthogonal polynomials, including multiple Hahn, Jacobi-Piñeiro, Laguerre of the first kind, and Meixner of the second kind, along with their hypergeometric representations and derives the corresponding recurrent finite Markov chains and time-reversed chains.

math.PR↗
arXiv2024

Classical multiple orthogonal polynomials for arbitrary number of weights and their explicit representation

This paper delves into classical multiple orthogonal polynomials with an arbitrary number of weights, including Jacobi-Piñeiro, Laguerre of both first and second kinds, as well as multiple orthogonal Hermite polynomials. Novel explicit expressions for nearest-neighbor recurrence coefficients, as well as the step line case, are provided for all these polynomial families. Furthermore, new explicit expressions for type I multiple orthogonal polynomials are derived for Laguerre of the second kind and also for multiple Hermite polynomials.

math.CA↗