Butzer, Paul L.; Higgins, J. R.; Stens, R. L. Sampling theory of signal analysis. (English) Zbl 0961.94009 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\(\bullet\) sampling of band-limited functions; Poisson’s summation formula\(\bullet\) sampling of derivatives and Hilbert transforms; multichannel sampling\(\bullet\) error estimates; truncation, amplitude, time-jitter errors\(\bullet\) sampling of not necessary band-limited functions; aliasing error\(\bullet\) Kramer’s generalized sampling theorem\(\bullet\) sampling of special functions and Riemann zeta function\(\bullet\) generalized sampling series\(\bullet\) behaviour of sampling series at jump discontinuities\(\bullet\) sampling in abstract spaces\({\phantom \bullet}\) – Hilbert space methods\({\phantom \bullet}\) – sampling on locally compact abelian groups.For the entire collection see [Zbl 0947.00008]. Reviewer: Gabriele Steidl (Mannheim) Cited in 28 Documents MSC: 94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010) 42A99 Harmonic analysis in one variable 42C99 Nontrigonometric harmonic analysis PDFBibTeX XMLCite \textit{P. L. Butzer} et al., in: Development of mathematics 1950--2000. Basel: Birk\-häu\-ser. 193--234 (2000; Zbl 0961.94009)