Kernel Decompositions for Schur Functions on the Polydisk

被引：4
|
作者：
Knese, Greg [1 ]
机构：
[1] Univ Calif Irvine, Irvine, CA 92697 USA
来源：
COMPLEX ANALYSIS AND OPERATOR THEORY | 2011年 / 5卷 / 04期
关键词：
Schur function; Polydisk; Polydisc; Reproducing kernel; Agler decomposition; Pick interpolation;
D O I：
10.1007/s11785-010-0048-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 semi-definite. It can always be split into two kernels possessing certain shift invariance properties.
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页码：1093 / 1111
页数：19
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