Michael Quellmalz: A generalization of the Funk–Radon transform to circles passing through a fixed point

Author(s):

Michael Quellmalz

Title:

Michael Quellmalz: A generalization of the Funk–Radon transform to circles passing through a fixed point

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 17, 2015

Mathematics Subject Classification:

    45Q05 []
    44A12 []

Abstract:

The Funk–Radon transform assigns to a function on the two-sphere its mean values along all great circles. We consider the following generalization: we replace the great circles by the small circles being the intersection of the sphere with planes containing a common point \u03b6 inside the sphere. If \u03b6 is the origin, this is just the classical Funk–Radon transform. We find two mappings from the sphere to itself that enable us to represent the generalized Radon transform in terms of the Funk–Radon transform. This representation is utilized to characterize the nullspace and range as well as to prove an inversion formula of the generalized Radon transform.

Keywords:

Radon transform, spherical means, Funk–Radon transform

Language:

English

Publication time:

12/2015