关于无限维空间的一个层级及其相关的Kolmogorov-Gelfand宽度
On a hierarchy of infinite-dimensional spaces and related Kolmogorov-Gelfand widths
AI总结：
本文通过引入基于高阶椭圆方程解的无限维空间新层级，将Kolmogorov的原始结果推广到多维情形，并研究了相关的Kolmogorov-Gelfand宽度。
摘要：
最近，由于Kolmogorov-Gelfand宽度理论与新兴的压缩感知领域密切相关，它受到了广泛关注。人们认识到宽度能够恰当地反映信号处理中数据的稀疏性。然而，多维函数论中宽度理论的基本问题以及多维信号分析理论中的类似问题仍未得到解决。本文通过引入基于高阶椭圆方程解的一个新的无限维空间层级，提供了Kolmogorov原始结果的多维推广。
英文摘要：
Recently the theory of widths of Kolmogorov-Gelfand has received a great deal of interest due to its close relationship with the newly born area of Compressed Sensing. It has been realized that widths reflect properly the sparsity of the data in Signal Processing. However fundamental problems of the theory of widths in multidimensional Theory of Functions remain untouched, as well as analogous problems in the theory of multidimensional Signal Analysis. In the present paper we provide a multidimensional generalization of the original result of Kolmogorov by introducing a new hierarchy of infinite-dimensional spaces based on solutions of higher order elliptic equation.
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