9 papers
Positive Bidiagonal Factorizations for Banded Markov Processes
Manuel Mañas, 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-Like Multiple Orthogonal Polynomials of Mixed Type
Manuel Mañas, Manuel Mañas
This article constructs a Bessel-like family of mixed-type multiple orthogonal polynomials for a matrix weight on the unit circle. Unlike a rank-one product weight, thi…
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…
Bivariate multiple orthogonal polynomials of mixed type on the step-line
Manuel Mañas, Miguel Rojas, Jianwen Wu
This article studies bivariate multiple orthogonal polynomials of the mixed type on the step-line. The analysis is based on the LU factorization of a moment matrix specifically ada…