Explicit solutions of division problems for matrices of polynomials

TL;DR

This paper develops explicit integral formulas for solving matrix polynomial division problems in several complex variables, providing degree estimates of solutions through analysis of Hefer forms.

Contribution

It introduces explicit integral representations for matrix polynomial division and establishes degree bounds using Hefer form estimates.

Findings

Derived integral solutions for matrix polynomial division

Provided degree estimates for solutions based on Hefer forms

Enhanced understanding of polynomial division in several complex variables

Abstract

We present integral representations of solutions to division problems involving matrices of polynomials in several complex variables. We also find estimates of the polynomial degree of the solutions by means of careful degree estimates of the so-called Hefer forms which are components of the representations.