Monotone Valuations on the Space of Convex Functions

• Autorzy: L. Cavallina , A. Colesanti
• Języki publikacji: EN

Abstrakty

EN

We consider the space Cn of convex functions u defined in Rn with values in R ∪ {∞}, which are lower semi-continuous and such that lim|x| } ∞ u(x) = ∞. We study the valuations defined on Cn which are invariant under the composition with rigid motions, monotone and verify a certain type of continuity. We prove integral representations formulas for such valuations which are, in addition, simple or homogeneous.

Słowa kluczowe

EN

convex functions; valuations; convex bodies; sub-level sets; intrinsic volumes

Kategorie tematyczne

• 26B25: Convexity, generalizations
• 52A41: Convex functions and convex programs
• 52B45: Dissections and valuations (Hilbert's third problem, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-03-28

zaakceptowano

2015-06-16

online

2015-07-31

Twórcy

autor

L. Cavallina

• Dipartimento di Matematica e Informatica “U.Dini", Viale Morgagni 67/A, 50134, Firenze, Italy

autor

A. Colesanti

• Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai 980-857, Japan

Bibliografia

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Identyfikatory

DOI

10.1515/agms-2015-0012