An inversion formula for the spherical transform in S2 for a special family of circles of integration

被引：0
|
作者：
Salman, Yehonatan [1 ]
机构：
[1] Bar Ilan Univ, Ramat Gan, Israel
来源：
ANALYSIS AND MATHEMATICAL PHYSICS | 2016年 / 6卷 / 01期
关键词：
D O I：
10.1007/s13324-015-0105-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, an inversion formula is obtained for the spherical transform which integrates functions, defined on the unit sphere S-2, on circles. The inversion formula is for the case where the circles of integration are obtained by intersections of S-2 with hyperplanes passing through a common point (a) over bar strictly inside S-2. In particular, this yields inversion formulas for two well-known special cases. The first inversion formula is for the special case where the family of circles of integration consists of great circles; this formula is obtained by taking (a) over bar = 0. The second inversion formula is for the special case where the circles of integration pass through a common point p on S-2; this formula is obtained by taking the limit (a) over bar -> p.
引用
收藏
页码：43 / 58
页数：16
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