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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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Official URL: https://dx.doi.org/10.1007/s11785-017-0701-5

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
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
Depositing User: Id for Latest eprints
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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