Nevanlinna-Pick Kernels and Localization
Functional Analysis
2016-10-07 v1
Abstract
We describe those reproducing kernel Hilbert spaces of holomorphic functions on domains in for which an analogue of the Nevanlinna-Pick theorem holds, in other words when the existence of a (possibly matrix-valued) function in the unit ball of the multiplier algebra with specified values on a finite set of points is equivalent to the positvity of a related matrix. Our description is in terms of a certain localization property of the kernel.
Cite
@article{arxiv.1610.01965,
title = {Nevanlinna-Pick Kernels and Localization},
author = {Jim Agler and John E. McCarthy},
journal= {arXiv preprint arXiv:1610.01965},
year = {2016}
}
Comments
in Proceedings of 17th International Conference on Operator Theory at Timisoara, 1998, Theta Foundation, Bucharest