Functional Covering Numbers

Shiri Artstein-Avidan; Boaz A. Slomka

doi:10.1007/s12220-019-00310-3

Functional Covering Numbers

Shiri Artstein-Avidan, Boaz A. Slomka

Mathematics discipline

Research output: Contribution to journal › Article › peer-review

Abstract

We define covering and separation numbers for functions. We investigate their properties, and show that for some classes of functions there is exact equality between separation and covering numbers. We provide analogues for various geometric inequalities on covering numbers, such as volume bounds, bounds connected with Hadwiger’s conjecture, and inequalities about M-positions for geometric log-concave functions. In particular we get strong versions of M-positions for geometric log-concave functions.

Original language	English
Pages (from-to)	1039-1072
Number of pages	34
Journal	Journal of Geometric Analysis
Volume	31
Issue number	1
DOIs	https://doi.org/10.1007/s12220-019-00310-3
State	Published - Jan 2021

Bibliographical note

Publisher Copyright:
© 2019, Mathematica Josephina, Inc.

Keywords

Covering numbers
Duality
Functionalization of geometry
Log-concave functions
M-position
Volume bounds

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10.1007/s12220-019-00310-3

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Functional Covering Numbers

Abstract

Bibliographical note

Keywords

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