Finite Blaschke product interpolation on the closed unit disc

Christer Glader*, Mikael Lindström

*Korresponderande författare för detta arbete

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10 Citeringar (Scopus)

Sammanfattning

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.

OriginalspråkEngelska
Sidor (från-till)417-427
Antal sidor11
TidskriftJournal of Mathematical Analysis and Applications
Volym273
Nummer2
DOI
StatusPublicerad - 15 sep. 2002
MoE-publikationstypA1 Tidskriftsartikel-refererad

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