Applications of Reproducing Kernel Hilbert Spaces-Bandlimited Signal Models

The finite energy Fourier-, Hankel-, sine-, and cosine-transformed bandlimited signals are specific realizations of the abstract reproducing kernel Hilbert space (RKHS). Basic properties of the abstract RKHS are applied to the detailed study of bandlimited signals. The relevancy of the reproducing kernel in extremum problems is discussed. New and known results in sampling expansions, minimum energy and non-uniform interpolations, and truncation error bounds are presented from a unified point of view of the RKHS. Some generalizations and extensions are stated.