TY - JOUR
T1 - Functional Covering Numbers
AU - Artstein-Avidan, Shiri
AU - Slomka, Boaz A.
N1 - Publisher Copyright:
© 2019, Mathematica Josephina, Inc.
PY - 2021/1
Y1 - 2021/1
N2 - 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.
AB - 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.
KW - Covering numbers
KW - Duality
KW - Functionalization of geometry
KW - Log-concave functions
KW - M-position
KW - Volume bounds
UR - http://www.scopus.com/inward/record.url?scp=85074868067&partnerID=8YFLogxK
U2 - 10.1007/s12220-019-00310-3
DO - 10.1007/s12220-019-00310-3
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AN - SCOPUS:85074868067
SN - 1050-6926
VL - 31
SP - 1039
EP - 1072
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 1
ER -