Multi-operator colligations and multivariate characteristic functions

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.

15pp

References in corpus (1)

• Infinite symmetric group and combinatorial descriptions of semigroups of double cosets

Cited by in corpus (8)

• Multiplication of conjugacy classes, colligations, and characteristic functions of matrix argument
• Topological groups and invariant measures
• Symmetric groups and checker triangulated surfaces
• Groups $GL(\infty )$ over finite fields and multiplications of double cosets
• On the group of infinite $p$-adic matrices with integer elements
• On double cosets of groups $GL(n)$ with respect to subgroups of block strictly triangular matrices
• Inner functions of matrix argument and conjugacy classes in unitary groups
• Several remarks on groups of automorphisms of free groups