Valuations on Manifolds and Integral Geometry
Valuations on Manifolds and Integral Geometry
复制标题
流形和积分几何的评估
DOI：
10.1007/s00039-010-0088-1
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发表时间：
2009
影响因子：
2.2
通讯作者：
S. Alesker
中科院分区：
文献类型：
--
作者：
S. Alesker
我们构造了新的操作拉回和推进的估值流形上的淹没和浸入。使用这些操作和产品的估值上的一个一般的Radon型变换的介绍。结果表明，光滑函数上的经典Radon变换和可构造函数上著名的Radon变换，就欧拉特征而言，都是这种新Radon变换的特殊情况。在真实的射影空间的一个特殊情况下证明了关于赋值的Radon变换的一个反演公式。这些业务的关系，又一个经典类型的积分几何，克罗夫顿和运动公式，表示。
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.