10 papers
Piñeiro mixed orthogonal polynomials and bidiagonal factorization
Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié-Moreno +1
We study mixed multiple orthogonal polynomials associated with rank-one matrices of measures and their recurrence relations. On the step line we identify the corresponding banded r…
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…
Spectral theory for Markov chains with transition matrix admitting a stochastic bidiagonal factorization
Amílcar Branquinho, Ana Foulquié-Moreno, Manuel Mañas
The recently established spectral Favard theorem for bounded banded matrices admitting a positive bidiagonal factorization is applied to a broader class of Markov chains with bound…
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 matrix factorisations related to multiple orthogonal polynomials
Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié-Moreno +2
We provide necessary and sufficient conditions for the Hessenberg recurrence matrix associated with a system of multiple orthogonal polynomials to admit a factorisation as a produc…
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…