Author:
Bernig Andreas,Hug Daniel
Abstract
AbstractWe prove new kinematic formulas for tensor valuations and simplify previously known Crofton formulas by using the recently developed algebraic theory of translation invariant valuations. The heart of the paper is the computation of the Alesker–Fourier transform on the large class of spherical valuations, which is achieved by differential-geometric and representation theoretical tools. We also describe in explicit form the product and convolution of tensor valuations.
Funder
Deutsche Forschungsgemeinschaft
Subject
Applied Mathematics,General Mathematics
Reference106 articles.
1. A product formula for valuations on manifolds with applications to the integral geometry of the quaternionic line;Comment. Math. Helv.,2009
2. Integral geometry of unitary area measures;Adv. Math.,2014
3. Some remarks on Legendrian rectifiable currents;Manuscripta Math.,1998
4. Valuations and Euler-type relations on certain classes of convex polytopes;Proc. Lond. Math. Soc. (3),1977
5. Continuous rotation invariant valuations on convex sets;Ann. of Math. (2),1999
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