7 papers
Bidiagonal Factorization of Banded Recursion Matrices for Mixed-Type Multiple Orthogonal Polynomials
AmÃlcar 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
AmÃlcar 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
AmÃlcar 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…
Bidiagonal matrix factorisations related to multiple orthogonal polynomials
AmÃlcar Branquinho, Juan E. F. DÃaz, 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…
Generalized semiclassical orthogonal polynomials on the unit circle: A Riemann-Hilbert perspective
AmÃlcar 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…
Matrix Bessel Biorthogonal Polynomials: A Riemann-Hilbert approach
AmÃlcar 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…