The Hadwiger theorem on convex functions, IV: The Klain approach

Abstract

New proofs of the Hadwiger theorem for smooth and for continuous valuations on convex functions are obtained, and the Klain-Schneider theorem on convex functions is established. In addition, an extension theorem for valuations defined on functions with lower dimensional domains is proved, and its connection to the Abel transform is explained.

References in corpus (4)

• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
• The support of dually epi-translation invariant valuations on convex functions
• The Hadwiger theorem on convex functions, III: Steiner formulas and mixed Monge-Ampère measures
• Smooth valuations on convex functions

Cited by in corpus (7)

• The Hadwiger theorem on convex functions, I
• Equivariant Endomorphisms of Convex Functions
• Additive kinematic formulas for convex functions
• Valuations on Convex Bodies and Functions
• Inequalities and counterexamples for functional intrinsic volumes and beyond
• A Klain-Schneider Theorem for Vector-Valued Valuations on Convex Functions
• The Legendre transform, the Laplace transform and valuations