箱样条与等变指标定理
Box splines and the equivariant index theorem
摘要：
在本文中，我们开始回顾与Box样条卷积的反演公式。在向量空间M中，与G的线性作用相关的各种空间关于紧环面G的等变上同调和等变K-理论都可以用群G的对偶或其李代数的对偶上的分布的向量空间来描述。从K-理论的态射上同调分析和托德类的乘法被证明是对应的操作（反卷积）反转半离散卷积与盒样条。最后，利用符号的无穷小指标确定了M上G-横截椭圆算子的指标的重数。
英文摘要：
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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