Inversion of spherical means and the wave equation in even dimensions

Details Inversion of spherical means and the wave equation in even dimensions Inversion of spherical means and the wave equation in even dimensions

2007-01-15

arxiv.org/abs/math/0701426v1

Mathematics

Analysis of PDEs

26 pages, 5 figures

Scientific paper

We establish inversion formulas of the so called filtered back-projection type to recover a function supported in the ball in even dimensions from its spherical means over spheres centered on the boundary of the ball. We also find several formulas to recover initial data of the form (f,0) (or (0,g)) for the free space wave equation in even dimensions from the trace of the solution on the boundary of the ball, provided the initial data has support in the ball.

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