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Complex Analysis and Operator Theory

, Volume 13, Issue 5, pp 2069–2093 | Cite as

Pick Interpolation on the Polydisc: Small Families of Sufficient Kernels

  • Gautam BharaliEmail author
  • Vikramjeet Singh Chandel
Article
  • 162 Downloads

Abstract

We address Pick’s interpolation problem on the unit polydisc in \(\mathbb {C}^n\), \(n\ge 2\), by characterizing all interpolation data that admit a \(\mathbb {D}\)-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.

Keywords

Dual algebra Kernels Pick–Nevanlinna interpolation Polydisc Weak-star topology 

Mathematics Subject Classification

Primary 32A25 46E20 Secondary 32A38 46J15 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia

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