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Nevanlinna-Pick Kernels and Localization (1610.01965v1)
Published 6 Oct 2016 in math.FA
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.