Sampling on the Sierpinski gasket.
Shannon's sampling theorem, incongruent residue classes and Plancherel's theorem
Sampling theory for multi-band signals is shown to have a logical structure similar to that of Fourier analysis.
Signal processing and sampling method for obtaining time series corresponding to higher order derivatives.
Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory
2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.We characterize Paley-Wiener-Schwartz space of entire functions as a union of three-parametric linear normed subspaces determined by the type of the entire functions, their polynomial asymptotic on the real line, and the index p ≥ 1 of a Sobolev type Lp-summability on the real line with an appropriate weight function. An entire function belonging to a sub-space of the decomposition is exactly recovered by a sampling series, locally...