Approximation von operatorgleichungen mit reprokernen

Abstract

In this paper we develop a method for the approximation of a broad class of operator equations by reproducing kernels. The relevant operators are defined on Hilbert spaces. Necessary and sufficient conditions for the convergence of the approximation are discussed in detail. The results can be applied-for example-to Fredholm integral operators of the first and second kind and to ordinary and partial differential operators of elliptic type. In this context we refer to [9] for methods to construct reproducing kernels.