Schur Functions and Inner Functions on the Bidisc

Authors

Ramlal Debnath, Indian Institute of Technology Bombay
Jaydeb Sarkar, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Computational Methods and Function Theory

Abstract

We study representations of inner functions on the bidisc from a fractional linear transformation point of view. We provide sufficient conditions, in terms of colligation matrices, for the existence of two-variable inner functions. Here the sufficient conditions are not necessary in general, and we prove a weak converse for rational inner functions that admit a one variable factorization. We present a classification of de Branges–Rovnyak kernels on the bidisc (which also works in the setting of the polydisc and the open unit ball of Cn, n≥ 1). We also classify, in terms of Agler kernels, two-variable Schur functions that admit a one variable factorization.

First Page

133

Last Page

163

DOI

https://10.1007/s40315-022-00460-6

Publication Date

3-1-2023

Comments

Open Access, Green

Recommended Citation

Debnath, Ramlal and Sarkar, Jaydeb, "Schur Functions and Inner Functions on the Bidisc" (2023). Journal Articles. 3840.
https://digitalcommons.isical.ac.in/journal-articles/3840