Irregular sampling and frames. (English) Zbl 0777.42009

Wavelets: a tutorial in theory and applications, Wavelet Anal. Appl. 2, 445-507 (1992).
[For the entire collection see Zbl 0744.00020.]
This article is a survey of sampling theory of band-limited functions from the point of view of frames. It largely expands the original article of the author and W. Heller [Note Mat. 10, No. Suppl. 1, 103-125 (1990; preceding review)]. The classical sampling theory of Paley and Wiener, Duffin and Schaeffer, and Beurling and Landau, as well as more recent contributions are put into a modern framework. Special emphasis is given to semi-explicit reconstruction formulae for the irregular sampling problem and the recent connection to wavelet theory.
The clear exposition together with ample discussion of the results and a comprehensive list of references make this review an excellent introduction to the subject.


42C15 General harmonic expansions, frames
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
42A65 Completeness of sets of functions in one variable harmonic analysis