A theory of composites perspective on matrix valued Stieltjes functions

TL;DR

This paper explores how operations in composite material analysis can be understood through continued fraction transforms of matrix-valued Stieltjes functions, linking physical processes to mathematical function transformations.

Contribution

It introduces a novel interpretation of composite material operations using elementary continued fraction transforms of matrix-valued Stieltjes functions.

Findings

Provides a mathematical framework connecting physical operations to continued fraction transforms.

Enhances understanding of matrix-valued Stieltjes functions in the context of composite materials.

Lays groundwork for future analytical techniques in composite material theory.

Abstract

A series of physically motivated operations appearing in the study of composite materials are interpreted in terms of elementary continued fraction transforms of matrix valued, rational Stieltjes functions.