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Schur Functions and Inner Functions on the Bidisc
Journal
Computational Methods and Function Theory
ISSN
16179447
Date Issued
2023-03-01
Author(s)
Debnath, Ramlal
Sarkar, Jaydeb
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.
Volume
23
Publication link
Subjects