Inversion of Spherical Means and the Wave Equation in Even Dimensions
نویسندگان
چکیده
Abstract. 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.
منابع مشابه
Ja n 20 07 Inversion of spherical means and the wave equation in even dimensions
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 from (f, 0) (or (0, g)) for the free space wave equation in even dimensions from the trace of the solution on the boun...
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عنوان ژورنال:
- SIAM Journal of Applied Mathematics
دوره 68 شماره
صفحات -
تاریخ انتشار 2007