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

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.