Spectral theory for bounded banded matrices with positive bidiagonal factorization and mixed multiple orthogonal polynomials

TL;DR

This paper establishes a spectral Favard theorem for bounded banded matrices with positive bidiagonal factorizations, linking them to mixed multiple orthogonal polynomials and providing a Gauss quadrature formula.

Contribution

It introduces a spectral Favard theorem for such matrices and connects their properties to mixed multiple orthogonal polynomials with positive measures.

Findings

Spectral properties of oscillatory matrices are characterized.

A positive bidiagonal factorization leads to a new class of orthogonal polynomials.

A mixed multiple Gauss quadrature formula with specific degrees of precision is derived.

Abstract

Spectral and factorization properties of oscillatory matrices leads to a spectral Favard theorem for bounded banded matrices, that admit a positive bidiagonal factorization, in terms of sequences of mixed multiple orthogonal polynomials with respect to a set positive Lebesgue-Stieltjes measures. A mixed multiple Gauss quadrature formula with corresponding degrees of precision is given.