Kernel Decompositions for Schur Functions on the Polydisk

Greg Knese

doi:10.1007/s11785-010-0048-7

Kernel Decompositions for Schur Functions on the Polydisk

Greg Knese

Department of Mathematics

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

4 Scopus citations

Abstract

A certain kernel (sometimes called the Pick kernel) associated to Schur functions on the disk is always positive semi-definite. A generalization of this fact is well-known for Schur functions on the polydisk. In this article, we show that the "Pick kernel" on the polydisk has a great deal of structure beyond being positive semidefinite. It can always be split into two kernels possessing certain shift invariance properties.

Original language	English
Pages (from-to)	1093-1111
Number of pages	19
Journal	Complex Analysis and Operator Theory
Volume	5
Issue number	4
DOIs	https://doi.org/10.1007/s11785-010-0048-7
State	Published - Dec 2011

Keywords

Agler decomposition
Pick interpolation
Polydisc
Polydisk
Reproducing kernel
Schur function

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10.1007/s11785-010-0048-7

Cite this

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AB - A certain kernel (sometimes called the Pick kernel) associated to Schur functions on the disk is always positive semi-definite. A generalization of this fact is well-known for Schur functions on the polydisk. In this article, we show that the "Pick kernel" on the polydisk has a great deal of structure beyond being positive semidefinite. It can always be split into two kernels possessing certain shift invariance properties.

KW - Agler decomposition

KW - Pick interpolation

KW - Polydisc

KW - Polydisk

KW - Reproducing kernel

KW - Schur function

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JO - Complex Analysis and Operator Theory

JF - Complex Analysis and Operator Theory

IS - 4

ER -

Kernel Decompositions for Schur Functions on the Polydisk

Abstract

Keywords

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