Abstract
The goal of this paper is to use the theory of reproducing-kernel Hilbert spaces to obtain a generalization of the prolate spheroidal wave functions (PSWFs). We then employ this generalization to obtain a sampling formula for a general class of bandlimited functions. As a special case, we obtain a sampling formula for bandlimited signals in N variables that includes a generalization of Walter and Shen's result on sampling with the PSWFs. Another special case of our result is to show that the N-dimensional generalized PSWFs obtained by Slepian can also be used to obtain a sampling series for functions bandlimited to the unit ball in ℝN. The truncation errors of these sampling series are also investigated.
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