Note on the Fenchel transform in the Heisenberg group

作者：Calogero A; Pini R^*

来源：Journal of Mathematical Analysis and Applications, 2010, 368(1): 69-79.

DOI：10.1016/j.jmaa.2010.03.001

• Heisenberg group
• Convexity
• Subdifferentiability
• Fenchel transform
• Abstract convexity

Given a real-valued function defined on the Heisenberg group H, we provide a definition of abstract convexity and Fenchel transform in H, that takes into account the sub-Riemannian structure of the group. In our main result, we prove that, likewise the classical case, a convex function can be characterized via its iterated Fenchel transform: the properties of the H-subdifferential play a crucial role.

• 出版日期2010-8-1