COMPLEX ANALYSIS AND THE FUNK TRANSFORM

The Funk transform is defined by integrating a func- tion on the two-sphere over its great circles. We use complex anal- ysis to invert this transform.

[1]  H. Bateman,et al.  The Solution of Partial Differential Equations by Means of Definite Integrals , 1904 .

[2]  P. Funk.  Über Flächen mit lauter geschlossenen geodätischen Linien , 1913 .

[3]  F. John.  The ultrahyperbolic differential equation with four independent variables , 1938 .

[4]  W. Schmid.  Homogeneous complex manifolds and representations of semisimple lie groups. , 1968, Proceedings of the National Academy of Sciences of the United States of America.

[5]  Roger Penrose,et al.  Solutions of the Zero-Rest-Mass Equations , 1969 .

[6]  R. Harvey.  The Theory of Hyperfunctions on Totally Real Subsets of a Complex Manifold with Applications to Extension Problems , 1969 .

[7]  V. Guillemin.  The radon transform on zoll surfaces , 1976 .

[8]  S. G. Gindikin,et al.  Integral geometry in affine and projective spaces , 1982 .

[9]  R. Penrose,et al.  Spinors and Space–Time: Subject and author index , 1984 .

[10]  S. Sternberg,et al.  An ultra-hyperbolic analogue of the Robinson-Kerr theorem , 1986 .

[11]  Some notes on the Radon transform and integral geometry , 1992 .

[12]  Contour integrals for the ultrahyperbolic wave equation , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[13]  P. Schapira,et al.  Radon–Penrose Transform for D-Modules , 1996 .

[14]  T. Bailey,et al.  Institute for Mathematical Physics Zero–energy Fields on Real Projective Space , 2022 .

[15]  G. Sparling.  Inversion for the Radon line transform in higher dimensions , 1998, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[16]  L. Mason,et al.  The Funk transform as a Penrose transform , 1999, Mathematical Proceedings of the Cambridge Philosophical Society.

[17]  A. D'agnolo,et al.  Real forms of the radon-penrose transform , 2000 .