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The three-point Pick-Nevanlinna interpolation problem on the polydisc

Chandel, Vikramjeet Singh (2018) The three-point Pick-Nevanlinna interpolation problem on the polydisc. In: COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 63 (9). pp. 1341-1352.

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Official URL: https://dx.doi.org/10.1080/17476933.2017.1370461

Abstract

We give a necessary and sufficient condition for the existence of a holomorphic interpolant, for prescribed three-point Pick-Nevanlinna data. This is equivalent, due to results of Agler-McCarthy and Knese, to the existence of an interpolating rational inner function on the unit polydisc. Characterizing the latter reduces the search for a three-point interpolant to finding a single rational inner function that satisfies a certain positivity condition and arises from a polynomial of a very special form. This in turn relies on a pair of results on the factorization of rational inner functions.

Item Type: Journal Article
Additional Information: Copyright of this article belong to TAYLOR & FRANCIS LTD, 2-4 PARK SQUARE, MILTON PARK, ABINGDON OR14 4RN, OXON, ENGLAND
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 20 Jul 2018 16:37
Last Modified: 20 Jul 2018 16:37
URI: http://eprints.iisc.ac.in/id/eprint/60263

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