关于球片变换

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS ACS Applied Bio Materials Pub Date : 2021-01-17 DOI:10.1142/s021953052150024x
B. Rubin
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引用次数: 4

摘要

我们研究了一个函数在n维单位球面上通过k维仿射平面经过北极在球面横截面上的积分的球切片变换。当k=n时,这些变换是众所周知的。我们考虑所有$1< k < n+1$,得到了在$n$维欧几里德空间中$(k-1)$维平面上的球面片变换与经典Radon-John变换之间的显式公式。利用这种联系,Radon-John变换的已知事实,如反演公式、支持定理、区域函数的表示等,可以在球片变换中重新表述。
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On the Spherical Slice Transform
We study the spherical slice transform which assigns to a function on the $n$-dimensional unit sphere the integrals of that function over cross-sections of the sphere by $k$-dimensional affine planes passing through the north pole. These transforms are well known when $k=n$. We consider all $1< k < n+1$ and obtain an explicit formula connecting the spherical slice transform with the classical Radon-John transform over $(k-1)$-dimensional planes in the $n$-dimensional Euclidean space. Using this connection, known facts for the Radon-John transform, like inversion formulas, support theorem, representation on zonal functions, and others, can be reformulated for the spherical slice transform.
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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