Dependence of Kolmogorov widths on the ambient space
Timur Oikhberg, Mikhail Ostrovskii
TL;DR
This paper investigates how the Kolmogorov widths of a compact set vary depending on the ambient Banach space in which they are considered.
Contribution
It provides new insights into the relationship between Kolmogorov widths and the geometry of the ambient space.
Findings
Kolmogorov widths depend significantly on the ambient space geometry
Results characterize the variation of widths across different Banach spaces
Theoretical bounds for widths in various spaces are established
Abstract
We study the dependence of the Kolmogorov widths of a compact set on the ambient Banach space.
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Taxonomy
TopicsAdvanced Banach Space Theory · Mathematical Approximation and Integration · Point processes and geometric inequalities