Nevanlinna-Pick Kernels and Localization

2016/10/06 by Agler, Jim, McCarthy, John E.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1610.01965

Abstract

We describe those reproducing kernel Hilbert spaces of holomorphic functions on domains in \Bbb C^d 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.

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