Let f be a continuous function on R n. If f has zero integral over the intersection of every sphere with a given subset A of R n and A lies in no affine plane of dimension n-2, then f vanishes identically. The condition on the dimension of A is sharp.
|Number of pages||9|
|Journal||Siberian Mathematical Journal|
|State||Published - Jul 2004|
Bibliographical noteFunding Information:
pp. 723–733, July–August, 2004. Original article submitted March 30, 2004. 0037-4466/04/4504–0597 ©c 2004 Plenum Publishing Corporation The authors were supported by the Israel Scientific Foundation (Grant 279/02–01). Dedicated to the 75th birthday of Professor Yu. G. Reshetnyak.
- dependence domain
- spherical mean
- wave equation