Inner-outer factorization of analytic matrix-valued functions

TL;DR

This paper explores the inner-outer factorization of analytic matrix-valued functions, emphasizing their representation via multiplicative integrals and discussing Potapov's theorem involving Blaschke-Potapov factors.

Contribution

It provides a detailed analysis of factor representations using multiplicative integrals and revisits Potapov's theorem for contractive matrix functions.

Findings

Representation of factors via multiplicative integrals

Exposition of Potapov's theorem for contractive functions

Connection between inner-outer factorization and multiplicative integral theory

Abstract

This is a study of inner-outer factorization for analytic matrix-valued functions focusing on representations of the factors in terms of multiplicative integrals. Included is a brief introduction to the theory of multiplicative integrals and an exposition of V. P. Potapov's representation theorem for contractive matrix-valued functions in terms of Blaschke-Potapov factors and multiplicative integrals.