Infinite-dimensional generalization of Kolmogorov widths

Details Infinite-dimensional generalization of Kolmogorov widths Infinite-dimensional generalization of Kolmogorov widths

2011-03-09

arxiv.org/abs/1103.1906v1

Mathematics

Numerical Analysis

17 pages

Scientific paper

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 Compressive Sensing 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 about the widths of an "ellipsoidal sets" consisting of functions defined on an interval.

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