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.

PDF JOU_FUN_ANA_274-2_2017.pdf - Published Version Restricted to Registered users only Download (0B) | Request a copy

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
Publication:	JOURNAL OF FUNCTIONAL ANALYSIS
Publisher:	10.1016/j.jfa.2017.09.013
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
Date Deposited:	13 Jan 2018 07:41
Last Modified:	13 Jan 2018 07:41
URI:	http://eprints.iisc.ac.in/id/eprint/58565

Actions (login required)

View Item