arXiv:0812.2753 Abstract | arXiv Analytics

arXiv:0812.2753 [math.FA]Abstract References Reviews Resources

Note on the Fenchel transform in the Heisenberg group

Published 2008-12-15, updated 2010-05-17Version 2

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.

Comments: The paper appeared in Journal of Mathematical Analysis and Applications, volume 368, issue 1, August 2010, pages 69-79.

Categories: math.FA, math.DG

Subjects: 52A01, 53C17, 26B25

Keywords: heisenberg group, abstract convexity, crucial role, main result, euclidean case

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