In the main theorem of this paper we show that any involution on the class of lower semi-continuous convex functions which is order-reversing, must be, up to linear terms, the well known Legendre transform.
Shiri Artstein-Avidan 1 ; Vitali Milman 1
@article{10_4007_annals_2009_169_661,
author = {Shiri Artstein-Avidan and Vitali Milman},
title = {The concept of duality in convex analysis, and the characterization of the {Legendre} transform},
journal = {Annals of mathematics},
pages = {661--674},
year = {2009},
volume = {169},
number = {2},
doi = {10.4007/annals.2009.169.661},
mrnumber = {2480615},
zbl = {1173.26008},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.169.661/}
}
TY - JOUR AU - Shiri Artstein-Avidan AU - Vitali Milman TI - The concept of duality in convex analysis, and the characterization of the Legendre transform JO - Annals of mathematics PY - 2009 SP - 661 EP - 674 VL - 169 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.169.661/ DO - 10.4007/annals.2009.169.661 LA - en ID - 10_4007_annals_2009_169_661 ER -
%0 Journal Article %A Shiri Artstein-Avidan %A Vitali Milman %T The concept of duality in convex analysis, and the characterization of the Legendre transform %J Annals of mathematics %D 2009 %P 661-674 %V 169 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.169.661/ %R 10.4007/annals.2009.169.661 %G en %F 10_4007_annals_2009_169_661
Shiri Artstein-Avidan; Vitali Milman. The concept of duality in convex analysis, and the characterization of the Legendre transform. Annals of mathematics, Tome 169 (2009) no. 2, pp. 661-674. doi: 10.4007/annals.2009.169.661
Cité par Sources :