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 Funktsional. Anal. i Prilozhen.: Year: Volume: Issue: Page: Find

 Funktsional. Anal. i Prilozhen., 2017, Volume 51, Issue 2, Pages 25–41 (Mi faa3441)

Multiplication of conjugacy classes, colligations, and characteristic functions of matrix argument

Yu. A. Neretinabcd

a Mathematical Department, University of Vienna, Vienna, Austria
b Institute for Theoretical and Experimental Physics, Moscow, Russia
c Mechanics and Mathematics Faculty, M. V. Lomonosov Moscow State University, Moscow, Russia
d Institute for Information Transmission Problems, Moscow, Russia

Abstract: We extend the classical construction of operator colligations and characteristic functions. Consider the group G of finitary block unitary matrices of order $\alpha+\infty+…+\infty$ ($m$ times) and its subgroup $K \cong U(\infty)$, which consists of block diagonal unitary matrices with the identity block of order $\alpha$ and a matrix $u \in U(\infty)$ repeated $m$ times. It turns out that there is a natural multiplication on the space $G$//$K$ of conjugacy classes. We construct “spectral data” of conjugacy classes, which visualize the multiplication and are sufficient for reconstructing a conjugacy class.

Keywords: characteristic function, colligation, spectral data, infinite-dimensional group, inner function, Grassmannian, Hermitian symmetric space, invariant theory.

 Funding Agency Grant Number Austrian Science Fund P22122P25142 Supported by FWF grants P22122 and P25142.

DOI: https://doi.org/10.4213/faa3441

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English version:
Functional Analysis and Its Applications, 2017, 51:2, 98–111

Bibliographic databases:

UDC: 517.986.4+512.745.2+517.986.9
Revised: 28.04.2016
Accepted:19.05.2016

Citation: Yu. A. Neretin, “Multiplication of conjugacy classes, colligations, and characteristic functions of matrix argument”, Funktsional. Anal. i Prilozhen., 51:2 (2017), 25–41; Funct. Anal. Appl., 51:2 (2017), 98–111

Citation in format AMSBIB
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