Abstract
We consider systems of functions obtained from contractions and shifts of a single function in spaces Lp(0, 1), 1 ≤ p < ∞. We obtained the results on Fourier-type series with integer coefficients with respect to the mentioned systems. The approximation of elements of spaces Lp(0, 1), 1 ≤ p < ∞, leads to the image compression, i.e., many coefficients vanish. Results of this paper also may be of interest for experts in digital information processing and transfer.
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