Valuations on Manifolds and Integral Geometry

被引：0
作者：
Semyon Alesker
机构：
[1] Tel Aviv University,Department of Mathematics, Sackler Faculty of Exact Sciences
来源：
Geometric and Functional Analysis | 2010年 / 20卷
关键词：
Valuations; manifolds; Radon transform; 52B45 (52A39, 53C65, 44A12);
D O I：
暂无
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学科分类号：
摘要：
We construct new operations of pull-back and push-forward on valuations on manifolds with respect to submersions and immersions. A general Radon-type transform on valuations is introduced using these operations and the product on valuations. It is shown that the classical Radon transform on smooth functions, and the well-known Radon transform on constructible functions, with respect to the Euler characteristic, are special cases of this new Radon transform. An inversion formula for the Radon transform on valuations has been proven in a specific case of real projective spaces. Relations of these operations to yet another classical type of integral geometry, Crofton and kinematic formulas, are indicated.
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页码：1073 / 1143
页数：70
相关论文
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