The Hadwiger Theorem on Convex Functions, I
Andrea Colesanti, Monika Ludwig, Fabian Mussnig
Abstract
Abstract A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on ${\mathbb{R}}^{n}$ is established. The valuations obtained are functional versions of the classical intrinsic volumes. For their definition, singular Hessian valuations are introduced.
Topics & Concepts
MathematicsRegular polygonConvex analysisDanskin's theoremPure mathematicsConvex optimizationFixed-point theoremBrouwer fixed-point theoremGeometryPoint processes and geometric inequalitiesFunctional Equations Stability ResultsAdvanced Banach Space Theory