Box splines and the equivariant index theorem (Q2841759)
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scientific article; zbMATH DE number 6192529
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Box splines and the equivariant index theorem |
scientific article; zbMATH DE number 6192529 |
Statements
Box splines and the equivariant index theorem (English)
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30 July 2013
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splines
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box splines
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deconvolution
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index theory
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equivariant \(K\)-theory
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equivariant cohomology
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Riemann-Roch
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elliptic operators
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pseudo-differential operator
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Todd class
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Splines and box-splines as objects from well-understood spaces of piecewise polynomials in more than one unknown create approximation spaces with interesting algebraic (e.g. Chapter 3) and geometric properties are studied. In this very nice paper, convolution operators with box-splines are studied as a suitable underlying method in order to analyse certain multiplicities of tori representations, obtained as indices of pseudo-differential operators. The box-splines are introduced from the algebraic point of view in the second chapter. Morphisms from \(K\)-theory to cohomology are also studied (Chapters 4 and 5). The aforementioned (de-)convolution operators related to the familiar multivariate polynomial box-splines are shown to correspond to multiplications by Todd classes.
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