A new realization of rational functions, with applications to linear combination interpolation, the Cuntz relations and kernel decompositions

Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz, Dan Volok

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce the following linear combination interpolation problem (LCI), which in case of simple nodes reads as follows: given (Formula presented.) distinct numbers (Formula presented.) and (Formula presented.) complex numbers (Formula presented.) and (Formula presented.) , find all functions (Formula presented.) analytic in an open set (depending on (Formula presented.) ) containing the points (Formula presented.) such that (Formula presented.) To this end, we prove a representation theorem for such functions (Formula presented.) in terms of an associated polynomial (Formula presented.). We give applications of this representation theorem to realization of rational functions and representations of positive definite kernels.

Original languageAmerican English
Pages (from-to)42-54
Number of pages13
JournalComplex Variables and Elliptic Equations
Volume61
Issue number1
DOIs
StatePublished - 2 Jan 2016

Keywords

  • Cuntz relations
  • Infinite products
  • Multipoint interpolation
  • Reproducing kernels

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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