Abstract
In the spaces $$L_{p}(0,1)$$ , $$1\leq p<\infty$$ , we investigate the systems consisting of contractions and shifts of one function. We study Fourier type series expansions with integer coefficients by such systems. The resulting decompositions have the property of image compression, that is, many their coefficients vanish. This study may also be of interest to the specialists in transmission and processing of digital information.
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