Pier, Jean-Paul (ed.), Development of mathematics 1950-2000. Basel: Birkhäuser. 193-234 (2000).
The paper gives a good short overview of results in sampling theory from the Whittaker-Kotel’nikov-Shannon sampling theorem to recent developments. In particular the authors consider
sampling of band-limited functions; Poisson’s summation formula
sampling of derivatives and Hilbert transforms; multichannel sampling
error estimates; truncation, amplitude, time-jitter errors
sampling of not necessary band-limited functions; aliasing error
Kramer’s generalized sampling theorem
sampling of special functions and Riemann zeta function
generalized sampling series
behaviour of sampling series at jump discontinuities
sampling in abstract spaces
– Hilbert space methods
– sampling on locally compact abelian groups.