Two Radius Support Theorem for the Sphere Transform

We prove support theorems and injectivity for the sphere transform on restricted sets of spheres. We consider spheres with restricted sets of centers and two fixed radii. The proof of these theorems is based on E. T. Quinto’s Ž1993, Israel J. Math., 353 363.microlocal regularity theorem and a theorem of L. H¨ormanderŽ1983, ‘‘The Analysis of Linear Partial Differential Operators I,’’ Springer-Verlag, Ber- lin New York.and M. Sato et al.Ž1973, ‘‘Hyperfunctions and Pseudodifferential Equations,’’ Lecture Notes in Math., Vol. 287, pp. 265 529, Springer-Verlag, Berlin New York..