6 citations · 14 across the 22 of their papers we have counts for
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Bidiagonal Factorization of Banded Recursion Matrices for Mixed-Type Multiple Orthogonal Polynomials
Amílcar Branquinho, Ana Foulquié-Moreno, Manuel Mañas
Given a banded matrix with subdiagonals and superdiagonals arising from the Gauss--Borel factorization $\mathscr{M}_N = \mathscr{L}_N^{-1}\mathscr{U}_N^{-1}…
Unbounded banded matrices, shifted positive bidiagonal factorizations, and mixed-type multiple orthogonality
Amílcar Branquinho, Ana Foulquié-Moreno, Manuel Mañas
This work extends Favard-type spectral representations for banded matrices beyond the bounded setting. It assumes that, for every , there exists a shift $s_N\g…
A Rodrigues Formula for Multiple Orthogonal Polynomials on the Simplex
Lidia Fernández, Ana Foulquié-Moreno, Juan Antonio Villegas
Rodrigues formulas play a central role in the construction of orthogonal polynomials associated with classical measures. In this paper, we introduce a family of multivariate multip…
Matrix Bessel Biorthogonal Polynomials: A Riemann-Hilbert approach
Amílcar Branquinho, Ana Foulquié-Moreno, Assil Fradi +1
We consider matrix orthogonal polynomials related to Bessel type matrices of weights that can be defined in terms of a given matrix Pearson equation. From a Riemann-Hilbert problem…
Bidiagonal factorization of recurrence banded matrices in mixed multiple orthogonality
Amílcar Branquinho, Juan EF Díaz, Ana Foulquié-Moreno +2
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 term…
Classical discrete multiple orthogonal polynomials: hypergeometric and integral representations
Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié-Moreno +2
This work explores classical discrete multiple orthogonal polynomials, including Hahn, Meixner of the first and second kinds, Kravchuk, and Charlier polynomials, with an arbitrary…
Integral and hypergeometric representations for multiple orthogonal polynomials
Amílcar Branquinho, Juan EF Díaz, Ana Foulquié-Moreno +2
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…
Generalized semiclassical orthogonal polynomials on the unit circle: A Riemann-Hilbert perspective
Amílcar Branquinho, Ana Foulquié-Moreno, Karina Rampazzi
In this work we show how to get advantage from the Riemann--Hilbert analysis in order to obtain first and second order differential equations for the orthogonal polynomials and ass…
Classical multiple orthogonal polynomials for arbitrary number of weights and their explicit representation
Amílcar Branquinho, Juan EF Díaz, Ana Foulquié-Moreno +1
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…
Banded totally positive matrices and normality for mixed multiple orthogonal polynomials
Amílcar Branquinho, Ana Foulquié-Moreno, Manuel Mañas
This paper serves as an introduction to banded totally positive matrices, exploring various characterizations and associated properties. A significant result within is the demonstr…
Lax-type pairs in the theory of bivariate orthogonal polynomials
Amílcar Branquinho, Ana Foulquié-Moreno, Teresa E. Pérez +1
Sequences of bivariate orthogonal polynomials written as vector polynomials of increasing size satisfy a couple of three term relations with matrix coefficients. In this work, intr…
Bidiagonal factorization of the recurrence matrix for the Hahn multiple orthogonal polynomials
Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié-Moreno +1
This paper explores a factorization using bidiagonal matrices of the recurrence matrix of Hahn multiple orthogonal polynomials. The factorization is expressed in terms of ratios in…
Banded matrices and their orthogonality
Amílcar Branquinho, Ana Foulquié-Moreno, Manuel Mañas
Banded bounded matrices, which represent non normal operators, of oscillatory type that admit a positive bidiagonal factorization are considered. To motivate the relevance of the o…
Matrix Orthogonal Polynomials: A Riemann--Hilbert approach
Amílcar Branquinho, Ana Foulquié-Moreno, Assil Fradi +1
In this work we show how to get advantage from the Riemann--Hilbert analysis in order to obtain information about the matrix orthogonal polynomials and functions of second kind ass…
Hahn multiple orthogonal polynomials of type I: Hypergeometrical expressions
Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié-Moreno +1
Explicit expressions for the Hahn multiple polynomials of type I, in terms of Kampé de Fériet hypergeometric series, are given. Orthogonal and biorthogonal relations are proven. Th…
Spectral theory for bounded banded matrices with positive bidiagonal factorization and mixed multiple orthogonal polynomials
Amílcar Branquinho, Ana Foulquié-Moreno, Manuel Mañas
Spectral and factorization properties of oscillatory matrices leads to a spectral Favard theorem for bounded banded matrices, that admit a positive bidiagonal factorization, in ter…
Positive bidiagonal factorization of tetradiagonal Hessenberg matrices
Amílcar Branquinho, Ana Foulquié-Moreno, Manuel Mañas
Recently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. In this paper conditions, in terms of…
Bidiagonal factorization of tetradiagonal matrices and Darboux transformations
Amílcar Branquinho, Ana Foulquié-Moreno, Manuel Mañas
Recently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. These type of matrices are oscillatory…
Hypergeometric Multiple Orthogonal Polynomials and Random Walks
Amílcar Branquinho, Juan E. Fernández-Díaz, Ana Foulquié-Moreno +1
The recently found hypergeometric multiple orthogonal polynomials on the step-line by Lima and Loureiro are shown to be random walk polynomials. It is proven that the corresponding…
Multiple Orthogonal Polynomials and Random Walks
Amílcar Branquinho, Ana Foulquié-Moreno, Manuel Mañas +2
Given a non-negative Jacobi matrix describing higher order recurrence relations for multiple orthogonal polynomials of type~II and corresponding linear forms of type I, a general s…