Infinite-dimensional generalization of Kolmogorov widths
It extends classical width theory to multidimensional settings, which is relevant for researchers in function theory and signal analysis.
The paper provides a multidimensional generalization of Kolmogorov's original result on widths of ellipsoidal sets, addressing fundamental problems in multidimensional function theory and signal analysis.
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.