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arXiv · 1012.1049

Box splines and the equivariant index theorem

C. De Concini·C. Procesi·M. Vergne
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Abstract

In this article, we start to recall the inversion formula for the convolution with the Box spline. The equivariant cohomology and the equivariant K-theory with respect to a compact torus G of various spaces associated to a linear action of G in a vector space M can be both described using some vector spaces of distributions, on the dual of the group G or on the dual of its Lie algebra. The morphism from K-theory to cohomology is analyzed and the multiplication by the Todd class is shown to correspond to the operator (deconvolution) inverting the semidiscrete convolution with a box spline. Finally, the multiplicities of the index of a G-transversally elliptic operator on M are determined using the infinitesimal index of the symbol.

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C. De Concini, C. Procesi, M. Vergne. 2010-12-05. Box splines and the equivariant index theorem. https://arxiv.org/abs/1012.1049

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