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.
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Communicated by Mihai Putinar.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Knese, G. Kernel Decompositions for Schur Functions on the Polydisk. Complex Anal. Oper. Theory 5, 1093–1111 (2011). https://doi.org/10.1007/s11785-010-0048-7
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DOI: https://doi.org/10.1007/s11785-010-0048-7