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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.

MSC:

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