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Funk transform
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Funk transform : ウィキペディア英語版
Funk transform
In the mathematical field of integral geometry, the Funk transform (also called Minkowski–Funk transform, Funk–Radon transform or spherical Radon transform) is an integral transform defined by integrating a function on great circles of the sphere. It was introduced by Paul Funk in 1916, based on the work of . It is closely related to the Radon transform. The original motivation for studying the Funk transform was to describe Zoll metrics on the sphere.
== Definition ==
Classically, the Funk transform is defined as follows. Let ''ƒ'' be a continuous function on the 2-sphere in R3. Then, for a unit vector x, let
:Ff(\mathbf) = \int_)} f(\mathbf)\,ds(\mathbf)
where the integral is carried out with respect to the arclength ''ds'' of the great circle ''C''(x) consisting of all unit vectors perpendicular to ''x'':
:C(\mathbf) = \\cdot\mathbf=0\}.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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