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Pesenson, Isaac Z.; Pesenson, Meyer Z.

Sampling, filtering and sparse approximations on combinatorial graphs. (English) Zbl 1218.42021

J. Fourier Anal. Appl. 16, No. 6, 921-942 (2010).
This paper firstly proves a Poincaré and Plancherel type inequality on graphs. Then by combining this inequality with the ideas of Duffin and Shaeffer’s theory, the authors give a sampling theorem. Finally with the filtering procedure, the authors obtain sparse approximations to functions in \(L_2(G)\).
Reviewer: Youming Liu (Beijing)

Cited in 15 Documents

MSC:

42C99 Nontrigonometric harmonic analysis
94A20 Sampling theory in information and communication theory
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
42C15 General harmonic expansions, frames
05C99 Graph theory

Keywords:

sparse approximation; combinatorial graphs; Paley-Wiener spaces
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\textit{I. Z. Pesenson} and \textit{M. Z. Pesenson}, J. Fourier Anal. Appl. 16, No. 6, 921--942 (2010; Zbl 1218.42021)
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