Laplace transforms and valuations

Abstract

It is proved that the classical Laplace transform is a continuous valuation which is positively GL$(n)$ covariant and logarithmic translation covariant. Conversely, these properties turn out to be sufficient to characterize this transform.

References in corpus (6)

• Monotone valuations on the space of convex functions
• Real-valued valuations on Sobolev spaces
• SL(n)-Contravariant $L_p$-Minkowski Valuations
• $L_p$-Blaschke Valuations
• Elementary moves on triangulations
• Non-trivial translation-invariant valuations on $L^{\infty }$

Cited by in corpus (17)

• Valuations on Convex Functions
• Minkowski valuations on convex functions
• A homogeneous decomposition theorem for valuations on convex functions
• Volume, Polar Volume and Euler Characteristic for Convex Functions
• The Hadwiger theorem on convex functions, IV: The Klain approach
• The Hadwiger theorem on convex functions, III: Steiner formulas and mixed Monge-Ampère measures
• The Hadwiger theorem on convex functions, I
• $\mathrm{SL}(\mathrm{n})$ covariant function-valued valuations
• Valuations on Log-Concave Functions
• Valuations on Convex Bodies and Functions
• Geometric valuation theory
• Affine function valued valuations
• Translation invariant valuations on quasi-concave functions
• A Klain-Schneider Theorem for Vector-Valued Valuations on Convex Functions
• The Legendre transform, the Laplace transform and valuations
• Unimodular Valuations beyond Ehrhart
• Orlicz mixed chord integrals