Note on the Fenchel transform in the Heisenberg group
Functional Analysis
2010-05-18 v2 Differential Geometry
Abstract
Given a real-valued function defined on the Heisenberg group, we provide a definition of abstract convexity and Fenchel transform that takes into account the sub-Riemannian structure of the group. In our main result, we prove that, likewise the Euclidean case, a convex function can be characterized via its iterated Fenchel transform; the properties of the H-subdifferential play a crucial role.
Cite
@article{arxiv.0812.2753,
title = {Note on the Fenchel transform in the Heisenberg group},
author = {A. Calogero and R. Pini},
journal= {arXiv preprint arXiv:0812.2753},
year = {2010}
}
Comments
The paper appeared in Journal of Mathematical Analysis and Applications, volume 368, issue 1, August 2010, pages 69-79.