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arXiv · 1608.03768

Projection functions, area measures and the Alesker-Fourier transform

Felix Dorrek·Franz E. Schuster
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Abstract

Dual to Koldobsky's notion of j-intersection bodies, the class of j-projection bodies is introduced, generalizing Minkowski's classical notion of projection bodies of convex bodies. A Fourier analytic characterization of j-projection bodies in terms of their area measures of order j is obtained. In turn, this yields an equivalent characterization of j-projection bodies involving Alesker's Fourier type transform on translation invariant smooth spherical valuations. As applications of these results, several basic properties of j-projection bodies are established and new non-trivial examples are constructed.

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Felix Dorrek, Franz E. Schuster. 2016-08-12. Projection functions, area measures and the Alesker-Fourier transform. https://arxiv.org/abs/1608.03768

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