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 these type of valuations.

Translation invariant valuations on quasi-concave functions / Colesanti, Andrea; Lombardi, Nico; Lukas, Parapatits. - In: STUDIA MATHEMATICA. - ISSN 0039-3223. - STAMPA. - 243:(2018), pp. 79-99. [10.4064/sm170323-7-7]

Translation invariant valuations on quasi-concave functions

Andrea Colesanti;Nico Lombardi;
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 these type of valuations.
2018
243
79
99
Colesanti, Andrea; Lombardi, Nico; Lukas, Parapatits
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1102101
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