Pick Interpolation on the Polydisc: Small Families of Sufficient Kernels

Bharali, Gautam and Chandel, Vikramjeet Singh (2019) Pick Interpolation on the Polydisc: Small Families of Sufficient Kernels. In: COMPLEX ANALYSIS AND OPERATOR THEORY, 13 (5). pp. 2069-2093.

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Abstract

We address Pick's interpolation problem on the unit polydisc in Cn, n >= 2, by characterizing all interpolation data that admit a D-valued interpolant in terms of a family of positive-definite kernels parametrized by a class of polynomials. This uses a duality approach that has been associated with Pick interpolation, together with some approximation theory. Furthermore, we use duality methods to understand the set of points on the n-torus at which the boundary values of a given solution to an extremal interpolation problem are not unimodular.

Item Type:	Journal Article
Publication:	COMPLEX ANALYSIS AND OPERATOR THEORY
Publisher:	SPRINGER BASEL AG
Additional Information:	coopyright for this article belongs to SPRINGER BASEL AG
Keywords:	Dual algebra; Kernels; Pick-Nevanlinna interpolation; Polydisc; Weak-star topology
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	05 Aug 2019 10:06
Last Modified:	05 Aug 2019 10:06
URI:	http://eprints.iisc.ac.in/id/eprint/63379

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