Sampling in a Hilbert space
Abbreviated Journal Title
Proc. Amer. Math. Soc.
Shannon's sampling theorem; interpolation and approximation in a Hilbert; space; frames and frame operators; Mathematics, Applied; Mathematics
An analog of the Whittaker-Shannon-Kotel'nikov sampling theorem is derived for functions with values in a separable Hilbert space. The proof uses the concept of frames and frame operators in a Hilbert space. One of the consequences of this theorem is that it allows us to derive sampling theorems associated with boundary-value problems and some homogeneous integral equations, which in turn gives us a generalization of another sampling theorem by Kramer.
Proceedings of the American Mathematical Society
"Sampling in a Hilbert space" (1996). Faculty Bibliography 1990s. 1814.