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.

引用

页码：131 / 142

页数：12

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