Transfer Functions for Pairs of Wandering Subspaces

TL;DR

This paper introduces transfer functions for pairs of wandering subspaces in operator theory, connecting them with characteristic functions and transfer functions from noncommutative Markov chains, highlighting their structure and special cases.

Contribution

It presents a unified framework linking transfer functions, characteristic functions, and noncommutative Markov chain models in operator theory.

Findings

Transfer functions are multi-Toeplitz in general.

Special cases yield multi-analytic functions.

The framework unifies different operator-theoretic concepts.

Abstract

To a pair of subspaces wandering with respect to a row isometry we associate a transfer function which in general is multi-Toeplitz and in interesting special cases is multi-analytic. Then we describe in an expository way how characteristic functions from operator theory as well as transfer functions from noncommutative Markov chains fit into this scheme.