Construction of reproducing kernels for analytic Hilbert spaces

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Abstract
The reproducing kernels of suitably chosen Hilbert spaces provide a simple but powerful way to generate approximations to functions on which linear data is given. These data may consist either of exact values (for the problem of interpolation) or of values subject to experimental error. For applications, it is important to be able to construct reproducing kernels which embody the information which is available from general considerations about the physics of the problem. Explicit methods are given here for construction of reproducing kernels for Hilbert spaces of analytic functions, these functions being characterized by various types of behavior on the boundary of their domain of holomorphy.