Integrals of Smooth and Analytic Functions over Minkowski ’ s Sums of Convex Sets

@inproceedings{Alesker1998IntegralsOS,
title={Integrals of Smooth and Analytic Functions over Minkowski ’ s Sums of Convex Sets},
author={Semyon Alesker},
year={1998}
}

This defines an operator MK̄ , which we will call a Minkowski operator. Denote by A(C) the Frechet space of entire functions in n variables with the usual topology of the uniform convergence on compact sets in C, and C(R) the Frechet space of r times differentiable functions on R with the topology of the uniform convergence on compact sets in R of all partial derivatives up to the order r (1 ≤ r ≤ ∞). The main results of this work are Theorems 1 and 3 below.