Inversion of some spherical cap radon transforms

Radon transforms on spheres have contributed to the eld of partial dierential equations as solutions to Darboux equation's and, under prescribed conditions, have served as imaging principles for Sonar, Radar, photo-acoustic imaging and the like. In this paper the inverses of Radon transforms dened on three classes of spherical caps (surfaces with boundary) are derived. Through the so-called Harmonic Component Decomposition of functions and the application of Funk-Hecke's theorem, the inversion procedure follows a route established long ago for the Radon transform on spheres intersecting a xed point. These results may open the way to new three-dimensional imaging processes, based on ionizing radiation properties