Abstract
We consider a class of weighted plane generalized Radon transforms Rf(γ)=∫f(x,u(ξ,η,x))m(ξ,η,x) dx, where the curve γ=γ (ξ,η) is defined by y=u(ξ,η,x), and m(ξ,η,x) is a given positive weight function. We prove local injectivity for this transform across a given curve γ 0 near a given point (x 0,y 0) on γ 0 for classes of curves and weight functions that are invariant under arbitrary smooth coordinate transformations in the plane.
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Dedicated to the memory of Leon Ehrenpreis.
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Boman, J. (2012). On Local Injectivity for Generalized Radon Transforms. In: Sabadini, I., Struppa, D. (eds) The Mathematical Legacy of Leon Ehrenpreis. Springer Proceedings in Mathematics, vol 16. Springer, Milano. https://doi.org/10.1007/978-88-470-1947-8_5
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DOI: https://doi.org/10.1007/978-88-470-1947-8_5
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-1946-1
Online ISBN: 978-88-470-1947-8
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