In this paper, we show that the expansions of functions from -Paley–Wiener type spaces in terms of the prolate spheroidal wave functions converge almost everywhere for , even in the cases when they might not converge in -norm. We thereby consider the classical Paley–Wiener spaces of functions whose Fourier transform is supported in and Paley–Wiener-like spaces of functions whose Hankel transform is supported in . As a side product, we show the continuity of the projection operator from to , .
"Almost everywhere convergence of prolate spheroidal series." Illinois J. Math. 64 (4) 467 - 479, December 2020. https://doi.org/10.1215/00192082-8622664