R^n上广义Radon变换的奇异值分解

数学物理学报 ›› 2004, Vol. 24 ›› Issue (3): 293-298.

R^n上广义Radon变换的奇异值分解

王金平

宁波大学理学院宁波 315211

出版日期:2004-06-22 发布日期:2004-06-22
基金资助:
宁波大学博士科研启动基金资助项目

The Singular Value Decomposition for Generalized Radon Transforms |in R^n

WANG Jin-Ping

Online:2004-06-22 Published:2004-06-22
Supported by:
宁波大学博士科研启动基金资助项目

摘要/Abstract

摘要：

当广义Radon变换限制在带权的平方可积函数空间时, 该文构造了一类广义 Radon 变换的奇异值分解,给出了它们的逆变换的一些结果, 从而导出了广义 Radon 变换的反演公式以及值域的特征.

关键词: 广义Radon变换;球谐函数;奇异值分解

Abstract:

The singular value decompositions for the generalized Radon transforms are constructed when they are restricted to function spaces which are square integrable on R^n with known weight function W_n, some results about inverse transforms of the generalized Radon transforms are given.Furthermore, the inversion formulae and characteristics of their ranges are also developed.

Key words: Generalized Radon transform, Spherical harmonics function; , Singular value deco mposition(SVD).

中图分类号:

44A15

王金平. R^n上广义Radon变换的奇异值分解[J]. 数学物理学报, 2004, 24(3): 293-298.

WANG Jin-Ping. The Singular Value Decomposition for Generalized Radon Transforms |in R^n[J]. Acta mathematica scientia,Series A, 2004, 24(3): 293-298.

[1]	王金平. Radon 型广义变换的反演及性态研究[J]. 数学物理学报, 2011, 31(3): 636-643.
[2]	张新红, 同登科. 关于Weber变换的推广[J]. 数学物理学报, 2010, 30(2): 509-516.