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