Radon-John transforms and spherical harmonics

被引：1
|
作者：
Estrada, Ricardo [1 ]
Rubin, Boris [1 ]
机构：
[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA
来源：
REPRESENTATION THEORY AND HARMONIC ANALYSIS ON SYMMETRIC SPACES | 2018年 / 714卷
关键词：
Gegenbauer-Chebyshev integrals; Radon-John transforms; Grass-mann manifolds; NONUNIQUENESS; RANGE; PLANE;
D O I：
10.1090/conm/714/14329
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The d-plane Radon-John transform takes functions on R-n to functions on the set of all d-dimensional planes in R-n by integration over these planes. We study the action of this transform on degenerate functions of the form f(x) = f(0)(r) Y-k(theta), where r = vertical bar x vertical bar > 0, theta = x/vertical bar x vertical bar, and Yk is a spherical harmonic of degree k. It is shown that the results for d < n - 1 are surprisingly different from those in the known case d = n - 1.
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页码：131 / 142
页数：12
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