Brauner, L., Hofstätter, G. C., & Ortega Moreno, O. A. (2024). Lefschetz operators on convex valuations. arXiv. https://doi.org/10.48550/arXiv.2402.14731
We investigate the action of Alesker's Lefschetz operators on translation invariant valuations on convex bodies. For scalar valued valuations, we describe this action on the level of Klain-Schneider functions by a Radon type transform, generalizing a result by Schuster and Wannerer. In the case of rotationally equivariant Minkowski valuations, the Lefschetz operators act on the generating function as a convolution transform. We show that the convolution kernel satisfies a Legendre type differential equation, and thus, is a strictly positive function that is smooth up to one point.
en
Project title:
Affine isoperimetrische Ungleichungen: P31448-N35 (FWF - Österr. Wissenschaftsfonds) Fixpunkt Probleme und isoperimetrische Ungleichungen: ESP 236-N (FWF - Österr. Wissenschaftsfonds)
