Spherical means with centers on a hyperplane in even dimensions
Data(s) |
01/03/2010
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Resumo |
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. |
Formato |
application/pdf |
Identificador |
http://eprints.iisc.ernet.in/26240/1/234.pdf Narayanan, EK and Rakesh, * (2010) Spherical means with centers on a hyperplane in even dimensions. In: Inverse Problems, 26 (3). |
Publicador |
Institute of Physics. |
Relação |
http://iopscience.iop.org/0266-5611/26/3/035014 http://eprints.iisc.ernet.in/26240/ |
Palavras-Chave | #Mathematics |
Tipo |
Journal Article PeerReviewed |