Morera Theorems for Spheres through a Point in CN
We prove Morera theorems for the Radon transform integrating on spheres through a point in ℂn. The proofs use spherical functions and integral equations techniques as well as a support theorem for a generalized Radon transform on hyperplanes.
Unable to display preview. Download preview PDF.
- [Ag1987]Agranovsky, M. (1978). Fourier transform on SL2(ℝ) and Morera type theorems, Soviet Math. Dokl., Vol. 19, (pages 1522-1526). Google Scholar
- [BCPZ]Berenstein, C.A., Chang, D-C., Pasucas, D., and Zalcman, L. (1992). Variations on the theorem of Morera, Contemp. Math., Vol. 137, (pages 63–78).Google Scholar
- [GrQ]Grinberg, E.L. and Quinto E., Morera Theorems for complex manifolds, preprint.Google Scholar
- [Jo]John, F. (1966). Plane Waves and Spherical Means, Interscience, New York.Google Scholar
- [Za1992]Zalcman, L. (1992), A bibliographic survey of the Pompeiu problem, Approximation of Solutions of Partial Differential Equations, B. Fuglede, M. Goldstein, W. Haussmann, W. K. Hayman, and L. Rogge, Editors, Vol. 365, Series C: Mathematics and Physical Sciences, NATO ASI Series, Kluwer Academic, Boston, (pages 185–94).Google Scholar