On essentially time and Hankel band-limited functions

In this paper, we show that the circular prolate spheroidal wave functions (CPSWFs) are the most concentrate energy function on (0, T) among Hankel band-limited functions, here T is a positive real number. Hence, they best approximate each function in the set of essentially time- and Hankel band-limited signals than any other subspace of L-2(0, +infinity). More precisely, using the theory of the CPSWFs, we show that the space spanned by the N first CPSWFs best approximate the set of essentially time- and Hankel band-limited signals than any other subspace of L-2(0, +infinity) of the same dimension N.