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H-convex distributions in stratified groups


Authors: A. Bonfiglioli, E. Lanconelli, V. Magnani and M. Scienza
Journal: Proc. Amer. Math. Soc. 141 (2013), 3633-3638
MSC (2010): Primary 46F10; Secondary 26A51, 22E25
DOI: https://doi.org/10.1090/S0002-9939-2013-11653-9
Published electronically: July 15, 2013
MathSciNet review: 3080185
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Abstract: We extend Dudley's characterization of convex functions to the framework of h-convex distributions on stratified groups. Precisely, we prove that every distribution with nonnegative horizontal Hessian is defined by an h-convex function.


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Additional Information

A. Bonfiglioli
Affiliation: Dipartimento Matematica, Università degli Studi di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy
Email: bonfigli@dm.unibo.it

E. Lanconelli
Affiliation: Dipartimento Matematica, Università degli Studi di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy
Email: lanconel@dm.unibo.it

V. Magnani
Affiliation: Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy
Email: magnani@dm.unipi.it

M. Scienza
Affiliation: Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy
Email: scienza@mail.dm.unipi.it

DOI: https://doi.org/10.1090/S0002-9939-2013-11653-9
Keywords: Distribution, convexity, stratified group
Received by editor(s): August 5, 2011
Received by editor(s) in revised form: January 11, 2012
Published electronically: July 15, 2013
Additional Notes: The third author was supported by the European Project ERC AdG *GeMeThNES*.
Communicated by: Tatiana Toro
Article copyright: © Copyright 2013 American Mathematical Society