13 papers
Positive Bidiagonal Factorizations and Mixed-Type Chebyshev Multiple Orthogonal Polynomials
Manuel Mañas
We characterize when a banded totally positive matrix admits a positive bidiagonal factorization. In finite dimension such a factorization always exists. For semi-infinite matrices…
Positive Bidiagonal Factorizations: Combinatorial Structure, Spectral Theory, and Matrix Continued Fractions
Manuel Mañas
Prescribed positive bidiagonal factorizations of semi-infinite banded matrices reveal spectral, approximation, and integrable structures for arbitrary lower and upper bandwidths. E…
An Askey Scheme for Jacobi Systems of Mixed Type: Laguerre Limits of the First and Second Kinds and Hermite Limits
Manuel Mañas
An Askey-type confluence scheme is developed for Jacobi multiple orthogonal systems of mixed type, with row weights and column weights. Rescaling the Jacobi variable near $…
An Askey-Type Confluence Scheme for Hahn-Like Multiple Orthogonality
Manuel Mañas
We embed the Jacobi-like and Laguerre-like systems for ordinary type-I/type-II multiple orthogonality introduced by Wolfs into a single Askey-type confluence scheme. Applying the B…
Positive Bidiagonal Factorizations for Banded Markov Processes
Manuel Mañas
An ordered positive bidiagonal factorization (PBF) is used to develop a spectral and probabilistic theory for Markov transition matrices of arbitrary finite bandwidth. The factors…
Bessel Multiple Orthogonal Polynomials of Mixed Type
Manuel Mañas
This article constructs a Bessel family of mixed-type multiple orthogonal polynomials for a matrix weight on the unit circle. Unlike a rank-one product weight, this mat…
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…
Uvarov Perturbations for Multiple Orthogonal Polynomials of the Mixed Type on the Step-Line
Manuel Mañas, Miguel Rojas
Uvarov-type perturbations for mixed-type multiple orthogonal polynomials on the step line are investigated within a matrix-analytic framework. The transformations considered involv…
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…
General Geronimus Perturbations for Mixed Multiple Orthogonal Polynomials
Manuel Mañas, Miguel Rojas
General Geronimus transformations, defined by regular matrix polynomials that are neither required to be monic nor restricted by the rank of their leading coefficients, are applied…
Toda and Laguerre-Freud equations for multiple discrete orthogonal polynomials with an arbitrary number of weights
Itsaso Fernández-Irisarri, Manuel Mañas
In this paper, we extend our investigation into semiclassical multiple discrete orthogonal polynomials by considering an arbitrary number of weights. We derive multiple versions of…