Infinite-dimensional generalization of Kolmogorov widths
Numerical Analysis
2011-03-11 v1 Analysis of PDEs
Functional Analysis
Spectral Theory
Abstract
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.
Cite
@article{arxiv.1103.1906,
title = {Infinite-dimensional generalization of Kolmogorov widths},
author = {Ognyan Kounchev},
journal= {arXiv preprint arXiv:1103.1906},
year = {2011}
}
Comments
17 pages