Methoden zur Bestimmung von Reprokernen

Methods to determine reproducing kernels. The explicit representation of continuous linear functionals on a Hilbert space by reprokernels is significant for interpolation and approximation. Starting with the kernels theorem, due to Schwartz, we develop methods to determine reprokernels for the Sobolev spaces W₂^k(Ω) if Ω R¹, and for some subspaces of W₂^k(Ω) if ΩRⁿ. Then we determine reprokernels for tensor products of Hilbert spaces. In addition to this we consider three types of limits of reprokernels.