We study expansions with integer coefficients of elements in the multidimensional spaces ##IMG## [http://ej.iop.org/images/1064-5632/84/4/796/IZV_84_4_796ieqn1.gif] {$L_p\{(0,1]^m\}$} , ##IMG## [http://ej.iop.org/images/1064-5632/84/4/796/IZV_84_4_796ieqn2.gif] {$1\leq p<\infty$} , in systems of translates and dilates of a single function. We describe models useful in applications, including those in multimodular spaces. The proposed approximation of elements in ##IMG## [http://ej.iop.org/images/1064-5632/84/4/796/IZV_84_4_796ieqn1.gif] {$L_p\{(0,1]^m\}$} , ##IMG## [http://ej.iop.org/images/1064-5632/84/4/796/IZV_84_4_796ieqn3.gif] {$1\leq p <\infty$} , has the property of image compression, that is, there are many zero coefficients in this expansion. The study may also be of interest to specialists in the transmission and processing of digital information since we find a simple algorithm f...

中文翻译：

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单个函数的平移和展开的整数扩展

我们研究多维空间中元素整数系数的展开## IMG ## [http://ej.iop.org/images/1064-5632/84/4/796/IZV_84_4_796ieqn1.gif] {$ L_p \ {（ 0,1] ^ m \} $}，## IMG ## [http://ej.iop.org/images/1064-5632/84/4/796/IZV_84_4_796ieqn2.gif] {$ 1 \ leq p <\ infty $}，在单个函数的转换和展开系统中，我们描述了适用于应用程序的模型，包括多模空间中的模型。## IMG ##中的拟议元素逼近[http://ej.iop.org/ images / 1064-5632 / 84/4/796 / IZV_84_4_796ieqn1.gif] {$ L_p \ {（0,1] ^ m \} $}，## IMG ## [http://ej.iop.org/images /1064-5632/84/4/796/IZV_84_4_796ieqn3.gif] {$ 1 \ leq p <\ infty $}，具有图像压缩的特性，也就是说，在这个扩展中有很多零系数。这项研究也可能引起数字信息传输和处理方面的专家的兴趣，因为我们发现了一种简单的算法，可以解决...