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The aim of this article is to introduce a method for recovering functions,defined on the $n - 1$ dimensional unit sphere $\Bbb S^{n - 1}$, using theirspherical transform, which integrates functions on $n - 2$ dimensionalsubspheres, on a prescribed family of subspheres of integration. This family ofsubspheres is obtained as follows, we take a spheroid $\Sigma$ inside $\BbbS^{n - 1}$ which contains the points $\pm e_{n}$ and then each subsphere ofintegration is obtained by the intersection of a hyperplane, which is tangentto $\Sigma$, with $\Bbb S^{n - 1}$. In particular, we obtain as a limitingcase, by shrinking the spheroid into its main axis, a method for recoveringfunctions in case where the subspheres of integration pass through a commonpoint in $\Bbb S^{n - 1}$.

Recovering Functions Defined on $\Bbb S^{n - 1}$ by Integration on Subspheres Obtained from Hyperplanes Tangent to a Spheroid