In the present paper, we consider sampling theorems on Banach function spaces. Here we obtain a necessary and sufficient condition. For the latter half of the paper, we consider sampling theorems in terms of wavelets.
"A Criterion of Sampling Theorems on Banach Function Spaces." Tokyo J. Math. 36 (1) 131 - 145, June 2013. https://doi.org/10.3836/tjm/1374497515