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Holomorphic functions on the symmetrized bidisk - Realization, interpolation and extension

Bhattacharyya, Tirthankar and Sau, Haripada (2017) Holomorphic functions on the symmetrized bidisk - Realization, interpolation and extension. In: JOURNAL OF FUNCTIONAL ANALYSIS, 274 (2). pp. 504-524.

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Official URL: http://dx.doi.org/10.1016/j.jfa.2017.09.013

Abstract

There are three new things in this paper about the open symmetrized bidisk G = {(z(1) + z(2), z(1)z(2)) : vertical bar z(1)vertical bar, vertical bar z(2)vertical bar < 1}They are, in the order in which they will be proved, (1) The Realization Theorem: A realization formula is demonstrated for every f in the norm unit ball of H-infinity(G). (2) The Interpolation Theorem: A Nevanlinna-Pick interpolation theorem is proved for data from the symmetrized bidisk and a specific formula is obtained for the interpolating function. (3) The Extension Theorem: Let V be a subset of the symmetrized bidisk G. Consider a function f that is holomorphic in a neighbourhood of V and bounded on V. A necessary and sufficient condition on f is obtained so that f possesses an H-infinity-norm preserving extension to the whole of G. (C) 2017 Elsevier Inc. All rights reserved.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the ACADEMIC PRESS INC ELSEVIER SCIENCE, 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: review EPrints Reviewer
Date Deposited: 13 Jan 2018 07:41
Last Modified: 13 Jan 2018 07:41
URI: http://eprints.iisc.ac.in/id/eprint/58565

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