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Translation invariant valuations on quasi-concave functions

Volume 243 / 2018

Andrea Colesanti, Nico Lombardi, Lukas Parapatits Studia Mathematica 243 (2018), 79-99 MSC: Primary 26B25; Secondary 52B45, 52A41. DOI: 10.4064/sm170323-7-7 Published online: 29 January 2018

Abstract

We study real-valued, continuous and translation invariant valuations defined on the space of quasi-concave functions of $N$ variables. In particular, we prove a homogeneous decomposition theorem of McMullen type, and we find a representation formula for those valuations which are $N$-homogeneous. Moreover, we introduce the notion of Klain’s functions for this type of valuations.

Authors

  • Andrea ColesantiDipartimento di Matematica e Informatica “U. Dini”
    University of Florence
    Viale Morgagni 67/A
    50134, Firenze, Italy
    e-mail
  • Nico LombardiDipartimento di Matematica e Informatica “U.Dini”
    University of Florence
    Viale Morgagni 67/A
    50134, Firenze, Italy
    e-mail
  • Lukas ParapatitsInstitute of Discrete Mathematics
    and Geometry
    Vienna University of Technology
    Wiedner Hauptstraße 8–10/104
    1040 Wien, Austria
    e-mail

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