Kinematic formulas for tensor valuations

By A. Bernig, Daniel Hug. 2014

52 citations recorded by the source corpus.

We 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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/aea6378154331b5fca7d67efbc3a6e7862d86a70

How researchers see this paper

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In Applied Mathematics

1. Thomas Wannerer
2. Franz E. Schuster
3. Yiming Zhao
4. Monika Ludwig
5. Christoph Haberl
6. A. Bernig
7. Judit Abardia
8. Lukas Parapatits

In Mathematical Physics

1. Thomas Wannerer
2. Franz E. Schuster
3. Yiming Zhao
4. Monika Ludwig
5. Judit Abardia

Citations in the corpus

• Minkowski valuations and generalized valuations (2015, methodology): “, more general, equivariant tensor valued valuations, where A = SymkRn (see [3, 10, 35, 67]). These results in turn were critical for the tremendous progress in integral geometry of recent years (see [5, 16, 17, 20, 35, 66] and the references therein). In 1974 Schneider [54, 55] first investigated va”