Abstract
We prove that the boundary of a bounded domain is a set of injectivity for the twisted spherical means on ℂn for a certain class of functions on ℂn. As a consequence we obtain results about injectivity of the spherical mean operator in the Heisenberg group and the complex Radon transform.
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Agranovsky, M.L., Berenstein, C., Chang, D.C., and Pascuas, D. (1994). Injectivity of the Pompeiu transform in the Heisenberg group,J. Anal. Math.,63, 131–173.
Agranovsky, M.L., Berenstein, C., and Kuchment, P. (1998). Approximation by spherical waves inL p-spaces,J. Geom. Anal.,6, 365–383.
Agranovsky, M.L. and Quinto, E.T. (1996). Injectivity sets for the Radon transform over circles and complete systems of radial functions,J. Funct Anal.,139, 383–414.
Agranovsky, M.L., Volchkov, V.V., and Zalcman, L.A. (1999). Conical uniqueness sets for the spherical Radon transform,Bull. London Math. Soc.,31, to appear.
Erdelyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F.G. (1953).Higher Transcendental Functions, Vol. 1, McGraw-Hill, New York.
Olver, F.M.J. (1974).Introduction to Asymptotics and Special Functions, Academic Press, New York.
Rawat, R. and Sitaram, A. (preprint). Injectivity sets for spherical means on ℝn and on symmetric spaces.
Thangavelu, S. (1991). Spherical means on the Heisenberg group and a restriction theorem for the symplectic Fourier transform,Revist. Mat. Ibero.,7, 135–155.
Thangavelu, S. (1993).Lectures on Hermite and Laguerre Expansions, Math Notes, Princeton University Press, Princeton, NJ.
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Communicated by Eric Todd Quinto
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Agranovsky, M.L., Rawat, R. Injectivity sets for spherical means on the Heisenberg group. The Journal of Fourier Analysis and Applications 5, 363–372 (1999). https://doi.org/10.1007/BF01259377
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DOI: https://doi.org/10.1007/BF01259377