Factorization theorems for dominated polynomials

TL;DR

This paper explores different factorization schemes for dominated polynomials, establishing the equivalence between a previously known theorem and an alternative linearization approach, highlighting the importance of proving their equivalence.

Contribution

It demonstrates the equivalence between the existing factorization theorem for dominated polynomials and a new linearization-based scheme, clarifying their relationship.

Findings

The original factorization theorem is equivalent to an alternative linearization scheme.

The alternative scheme's effectiveness depends on establishing their equivalence.

The paper emphasizes the necessity of proving equivalence for the alternative scheme to be satisfactory.

Abstract

In this note we prove that the factorization theorem for dominated polynomials previously proved by the authors is equivalent to an alternative factorization scheme that uses classical linear techniques and a linearization process. However, this alternative scheme is shown not to be satisfactory until the equivalence is proved.