Finite Blaschke product interpolation on the closed unit disc

Christer Glader*, Mikael Lindström

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

9 Citations (Scopus)

Abstract

We show how to construct all finite Blaschke product solution and the minimal scaled Blaschke product solution to the Nevanlinna-Pick interpolation problem in the open unit disc by solving eigenvalue problems of the interpolation data. Based on a result of Jones and Ruscheweyh we note that there always exists a finite Blaschke product of degree at most n - 1 that maps n distinct points in the closed unit disc, of which at least one is on the unit circle, into n arbitrary points in the closed unit disc, provided that the points inside the unit circle form a positive semi-definite Pick matrix of full rank. Finally, we discuss a numerical limiting procedure.

Original languageEnglish
Pages (from-to)417-427
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume273
Issue number2
DOIs
Publication statusPublished - 15 Sep 2002
MoE publication typeA1 Journal article-refereed

Keywords

  • Finite Blaschke product
  • Interpolation

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