Nevanlinna-Pick Kernels and Localization [article]

Jim Agler, John E. McCarthy
2016 arXiv   pre-print
We describe those reproducing kernel Hilbert spaces of holomorphic functions on domains in 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.
arXiv:1610.01965v1 fatcat:q5bkk57zrjab3hdpqxfomkroka