The Takagi problem on the disk and bidisk

Jim Agler; Joseph A. Ball; John E. McCarthy

The Takagi problem on the disk and bidisk

Jim Agler, Joseph A. Ball, John E. McCarthy

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

Abstract

We give a new proof on the disk that a Pick problem can be solved by a rational function that is unimodular on the unit circle and for which the number of poles inside the disk is no more than the number of non-positive eigenvalues of the Pick matrix. We use this method to find rational solutions to Pick problems on the bidisk.

Original language	English
Pages (from-to)	63-78
Number of pages	16
Journal	Acta Scientiarum Mathematicarum
Volume	79
Issue number	1-2
State	Published - 2013

Keywords

Degenerate Pick problem
Nevanlinna-Pick interpolation
Rational interpolation
Takagi problem

Cite this

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AB - We give a new proof on the disk that a Pick problem can be solved by a rational function that is unimodular on the unit circle and for which the number of poles inside the disk is no more than the number of non-positive eigenvalues of the Pick matrix. We use this method to find rational solutions to Pick problems on the bidisk.

KW - Degenerate Pick problem

KW - Nevanlinna-Pick interpolation

KW - Rational interpolation

KW - Takagi problem

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The Takagi problem on the disk and bidisk

Abstract

Keywords

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