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.

中文翻译：

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一个函数的收缩和位移系统的整数系数级数

摘要

在空间\（L_ {p}（0,1）\），\（1 \ leq p <\ infty \）中，我们研究了由一个函数的收缩和移位组成的系统。我们通过这种系统研究了具有整数系数的傅立叶类型级数展开。所得到的分解具有图像压缩的特性，也就是说，许多分解系数都消失了。这项研究也可能对数字信息的传输和处理方面的专家感兴趣。