Computational Methods and Function Theory 6 (2006), No. 2, 493--511
Copyright Heldermann Verlag 2006
Gunter Semmler
semmler@math.tu-freiberg.de , Zentrum Mathematik M6, Technische Universität München, Boltzmannstraße 2, 85747 Garching, Germany.
Elias Wegert
wegert@math.tu-freiberg.de , Faculty of Mathematics and Computer Science, University of Mining and Technology, 09596 Freiberg, Germany.
We study a version of the classical Nevanlinna-Pick interpolation problem for Blaschke products where all interpolation points are located on the boundary of the unit disc. It turns out that all problems fall into three classes which are distinguished by the minimal degree of the interpolating function. The properties of the classes are studied in some detail. In particular it is shown that exactly one class consists of well-posed problems. An algorithm for classifying a given boundary interpolation problem is developed and a procedure for finding a solution with minimal degree for the generic class of regular problems is described.
Keywords: Blaschke product, Nevanlinna-Pick interpolation, boundary interpolation, rational interpolation.
MSC 2000: 30E05, 30D50, 41A05.
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