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Abstract: Given a real valued function on R^n we study the problem of recovering thefunction from its spherical means over spheres centered on a hyperplane. An oldpaper of Bukhgeim and Kardakov derived an inversion formula for the odd n casewith great simplicity and economy. We apply their method to derive an inversionformula for the even n case. A feature of our inversion formula, for the even ncase, is that it does not require the Fourier transform of the mean values orthe use of the Hilbert transform, unlike the previously known inversionformulas for the even n case. Along the way, we extend the isometry identity ofBukhgeim and Kardakov for odd n, for solutions of the wave equation, to theeven n case.



Autor: E K Narayanan, Rakesh

Fuente: https://arxiv.org/







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