Abstract
Suppose n > 1 is an odd integer, f is a smooth function supported in a ball B with boundary S, and u is the solution of the initial value problem We characterize the range of the map f ↦ u|S×[0,∞) and give a stable scheme for the inversion of this map. This also characterizes the range of the map sending f to its mean values over spheres centred on S.
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