Abstract
In this note, we study the operator norm of the generalized spherical Radon transform, defined by a smooth measure on the underlying incidence variety. In particular, we prove that for small perturbations of the measure, the spherical Radon transform remains an isomorphism between the corresponding Sobolev spaces.
Mathematical Subject Classifications (2010): 44A12, 53C65
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Acknowledgements
I would like to thank Semyon Alesker for numerous illuminating discussions, Victor Palamodov for his help with Fourier integral operators, and Alon Nishry for a useful suggestion. Finally, I want to thank Vitali Milman for his encouragement and interest in this work.
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Faifman, D. (2013). On a Stability Property of the Generalized Spherical Radon Transform. In: Ludwig, M., Milman, V., Pestov, V., Tomczak-Jaegermann, N. (eds) Asymptotic Geometric Analysis. Fields Institute Communications, vol 68. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6406-8_5
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DOI: https://doi.org/10.1007/978-1-4614-6406-8_5
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