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math.MG2024
The Klain approach to zonal valuations
Leo Brauner, Georg C. Hofstätter, Oscar Ortega-Moreno
We show an analogue of the Klain-Schneider theorem for valuations that are invariant under rotations around a fixed axis, called zonal. Using this, we establish a new integral repr…
math.MG2024
Lefschetz operators on convex valuations
Leo Brauner, Georg C. Hofstätter, Oscar Ortega-Moreno
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…