Interpolation for multipliers on reproducing kernel Hilbert spaces

Bolotnikov, Vladimir

doi:10.1090/S0002-9939-02-06899-5

Interpolation for multipliers on reproducing kernel Hilbert spaces
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Proc. Amer. Math. Soc. 131 (2003), 1373-1383 Request permission

Abstract:

All solutions of a tangential interpolation problem for contractive multipliers between two reproducing kernel Hilbert spaces of analytic vector-valued functions are characterized in terms of certain positive kernels. In a special important case when the spaces consist of analytic functions on the unit ball of $\mathbb {C}^d$ and the reproducing kernels are of the form $(1-\langle z,w\rangle ^{-1})I_p$ and $(1-\langle z,w\rangle )^{-1}I_q$, the characterization leads to a parametrization of the set of all solutions in terms of a linear fractional transformation.

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