Spherical means with centers on a hyperplane in even dimensions


Autoria(s): Narayanan, EK; Rakesh, *
Data(s)

01/03/2010

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