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Iterative reconstructions in irregular sampling with derivatives. (English) Zbl 0886.42023

Summary: Finite energy band-limited functions are reconstructed iteratively from nonuniform sample values of the functions and its derivatives. It is shown that the maximum gap allowed between the sampling points increases linearly with the number of derivatives considered. Moreover, a more precise result is presented for the first derivative case and another reconstruction of the functions using the frame algorithm is deduced.

MSC:

42C15 General harmonic expansions, frames
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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