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Spherical means with centers on a hyperplane in even dimensions

Narayanan, EK and Rakesh, * (2010) Spherical means with centers on a hyperplane in even dimensions. In: Inverse Problems, 26 (3).

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Official URL: http://iopscience.iop.org/0266-5611/26/3/035014

Abstract

Given a real-valued function on R-n we study the problem of recovering the function from its spherical means over spheres centered on a hyperplane. An old paper of Bukhgeim and Kardakov derived an inversion formula for the odd n case with great simplicity and economy. We apply their method to derive an inversion formula for the even n case. A feature of our inversion formula, for the even n case, is that it does not require the Fourier transform of the mean values or the use of the Hilbert transform, unlike the previously known inversion formulas for the even n case. Along the way, we extend the isometry identity of Bukhgeim and Kardakov for odd n, for solutions of the wave equation, to the even n case.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Institute of Physics.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 30 Mar 2010 10:47
Last Modified: 19 Sep 2010 05:57
URI: http://eprints.iisc.ernet.in/id/eprint/26240

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