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V. N. Stepanov

First-kind equations on a sphere and some problems of convex geometry

The properties of integral operators (with a kernel depending on scalar product) acting on Banach spaces of measures and functions on the sphere S^n-1 are studied. A theorem of unique solvability of a first-kind equation for measure is proved. Asymptotic formulae for eigenvalues of the kernel are derived. The results are used in proving theorems on the unique reconstructibility of a closed convex hypersurface from its curvature integrals and on its smoothness. Existence of a centrally symmetric closed convex hypersurface with a given curvature integral of projection is also demonstrated.

Journal of Inverse and Ill-posed Problems, Walter de Gruyter

Print ISSN: 0928-0219
Volume: 11, 09/2003
Pages: 289 - 310

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