SAMPLING IN A HILBERT-SPACE

An analog of the Whittaker-Shannon-Kotel'nikov sampling theorem is der ived for functions with values in a separable Hilbert space. The proof uses the concept of frames and frame operators in a Hilbert space. On e of the consequences of this theorem is that it allows us to derive s ampling theorems associated with boundary-value problems and some homo geneous integral equations, which in turn gives us a generalization of another sampling theorem by Kramer.