The cylindrical fourier transform

Abstract

The aim of this paper is to show the application potential of the cylindrical Fourier transform, which was recently devised as a new integral transform within the context of Clifford analysis. Next to the approximation approach where, using density arguments, the spectrum of various types of functions and distributions may be calculated starting from the cylindrical Fourier images of the L 2-basis functions in m, direct computation methods are introduced for specific distributions supported on the unit sphere, and an illustrative example is worked out. © 2010 Springer-Verlag London Limited.