The Hadwiger theorem on convex functions, IV: The Klain approach
Andrea Colesanti, Monika Ludwig, Fabian Mussnig
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 domain is proved, and its connection to the Abel transform is explained.
Topics & Concepts
MathematicsDanskin's theoremEffective domainRegular polygonConvex analysisExtension (predicate logic)Pure mathematicsMathematical proofConnection (principal bundle)Convex functionKrein–Milman theoremDiscrete mathematicsBrouwer fixed-point theoremFixed-point theoremConvex optimizationGeometryComputer scienceProgramming languageAdvanced Banach Space TheoryFunctional Equations Stability ResultsPoint processes and geometric inequalities