On the Nevanlinna-Pick interpolation problem for generalized Stieltjes functions

Daniel Alpay; Vladimir Bolotnikov; Aad Dijksma

doi:10.1007/BF01257874

On the Nevanlinna-Pick interpolation problem for generalized Stieltjes functions

Daniel Alpay, Vladimir Bolotnikov, Aad Dijksma

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

The solutions of the Nevanlinna-Pick interpolation problem for generalized Stieltjes matrix functions are parametrized via a fractional linear transformation over a subset of the class of classical Stieltjes functions. The fractional linear transformation of some of these functions may have a pole in one or more of the interpolation points, hence not all Stieltjes functions can serve as a parameter The set of excluded parameters is characterized in terms of the two related Pick matrices.

Original language	English
Pages (from-to)	379-408
Number of pages	30
Journal	Integral Equations and Operator Theory
Volume	30
Issue number	4
DOIs	https://doi.org/10.1007/BF01257874
State	Published - 1 Jan 1998

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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abstract = "The solutions of the Nevanlinna-Pick interpolation problem for generalized Stieltjes matrix functions are parametrized via a fractional linear transformation over a subset of the class of classical Stieltjes functions. The fractional linear transformation of some of these functions may have a pole in one or more of the interpolation points, hence not all Stieltjes functions can serve as a parameter The set of excluded parameters is characterized in terms of the two related Pick matrices.",

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AU - Dijksma, Aad

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AB - The solutions of the Nevanlinna-Pick interpolation problem for generalized Stieltjes matrix functions are parametrized via a fractional linear transformation over a subset of the class of classical Stieltjes functions. The fractional linear transformation of some of these functions may have a pole in one or more of the interpolation points, hence not all Stieltjes functions can serve as a parameter The set of excluded parameters is characterized in terms of the two related Pick matrices.

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On the Nevanlinna-Pick interpolation problem for generalized Stieltjes functions

Abstract

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