Matrix biorthogonal polynomials, associated polynomials and functions of the second kind

2017/08/04 by Amílcar Branquinho, Branquinho, Amilcar, Juan Carlos García-Ardila +3
Mathematics · Computer Science · #Mathematical functions and polynomials #Matrix Theory and Algorithms #Iterative Methods for Nonlinear Equations

paper · pdf · doi:10.48550/arxiv.1708.01637

Abstract

In this work the interplay between matrix biorthogonal polynomials with respect to a matrix of linear functionals, the k-th associated matrix polynomials and the second kind matrix functions, is studied in terms of quasideterminants. A sort of Poincaré's theorem for the ratio of two consecutive matrix functions solutions of a linear difference equation is also presented. Some new formulas connecting these families of matrix functions are given.

Citations

• Sur les Equations Lineaires aux Differentielles Ordinaires et aux Differences Finies

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