Characterizing the dual mixed volume via additive functionals

Carla Peri, Paolo Dulio, Richard J. Gardner

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

9 Citazioni (Scopus)

Abstract

Integral representations are obtained of positive additive functionals on finite products of the space of continuous functions (or of bounded Borel functions) on a compact Hausdorff space. These are shown to yield characterizations of the dual mixed volume, the fundamental concept in the dual Brunn-Minkowski theory. The characterizations are shown to be best possible in the sense that none of the assumptions can be omitted. The results obtained are in the spirit of a similar characterization of the mixed volume in the classical Brunn- Minkowski theory, obtained recently byMilman and Schneider, but the methods employed are completely different.
Lingua originaleEnglish
pagine (da-a)69-91
Numero di pagine23
RivistaIndiana University Mathematics Journal
Volume2016/Volume 65
DOI
Stato di pubblicazionePubblicato - 2016

Keywords

  • Additive functional
  • Brunn-Minkowski theory
  • Convex body
  • Dual Brunn-Minkowski theory
  • Dual mixed volume
  • Mixed volume
  • Positive functional
  • Star body
  • Star set

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