The object of this study is an integral operator *\mathcal{S}* which averages functions in the Euclidean upper half-space *\mathbb{R}_{+}^{n}* over the half-spheres centered on the topological boundary *\partial \mathbb{R}_{+}^{n}*. By generalizing Norton's approach to the inversion of arc means in the upper half-plane, we intertwine *\mathcal{S}* with a convolution operator... Show more

October 8, 2009

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Inversion of the Spherical Mean Transform with Sources on a Hyperplane

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