Multi-operator colligations and multivariate characteristic functions

TL;DR

This paper develops a framework for characteristic functions associated with operator colligations and double cosets, revealing semigroup structures of matrix-valued functions in matrix balls within spectral theory.

Contribution

It introduces characteristic functions for double cosets in the spectral theory of non-self-adjoint operators, extending the concept of operator colligations to a semigroup setting.

Findings

Constructed characteristic functions for double cosets.

Established semigroup structures of matrix-valued functions.

Linked operator colligations with infinite-dimensional group operations.

Abstract

In the spectral theory of non-self-adjoint operators there is a well-known operation of product of operator colligations. Many similar operations appear in the theory of infinite-dimensional groups as multiplications of double cosets. We construct characteristic functions for such double cosets and get semigroups of matrix-valued functions in matrix balls.