Convolutions and multiplier transformations of convex bodies
By Franz E. Schuster. 2007
82 citations recorded by the source corpus.
Rotation intertwining maps from the set of convex bodies in into itself that are continuous linear operators with respect to Minkowski and Blaschke addition are investigated. The main focus is on Blaschke-Minkowski homomorphisms. We show that such maps are represented by a spherical convolution operator. An application of this representation is a complete classification of all even Blaschke-Minkowski homomorphisms which shows that these maps behave in many respects similar to the well known projection body operator. Among further applications is the following result: If an even Blaschke-Minkowski homomorphism maps a convex body to a polytope, then it is a constant multiple of the projection body operator
Subfields: Applied Mathematics, Astronomy and Astrophysics
View Paper: https://www.semanticscholar.org/paper/f4cd825d104397e1f0afe37a03840c57188b7a28
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In Applied Mathematics
- Thomas Wannerer
- Monika Ludwig
- Franz E. Schuster
- Yiming Zhao
- Christoph Haberl
- Judit Abardia
- Lukas Parapatits
- Deane Yang
In Astronomy and Astrophysics
Citations in the corpus
- Valuations and Busemann{Petty Type Problems (2008, methodology): “This observation led in [62] to the following result, contrasting Theorem 3.”
- Volume inequalities and additive maps of convex bodies (2006, methodology): “The representation theorem for Blaschke-Minkowski homomorphisms is (see [ 37 ])”
- Valuations on Sobolev spaces (2012, background): “Also note that if we replace GL(n) contravariance by SO(n) covariance, there is a much larger class of valuations (see, for example, [52]).”
- Minkowski valuations and generalized valuations (2015, methodology): “6) is still open (see [59] for more information).”