Kernel decompositions for Schur functions on the polydisk
Complex Variables
2013-02-06 v1 Functional Analysis
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 semi-definite. It can always be split into two kernels possessing certain shift invariance properties.
Cite
@article{arxiv.0909.1828,
title = {Kernel decompositions for Schur functions on the polydisk},
author = {Greg Knese},
journal= {arXiv preprint arXiv:0909.1828},
year = {2013}
}
Comments
18 pages