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.
Editor-in-Chief: Kabanikhin, Sergey I.
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First-kind equations on a sphere and some problems of convex geometry
V. N. Stepanov∗
∗Omsk State Technical University. E-Mail: stepaw49@rol.ru
Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 11, Issue 3, Pages 289–310, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/156939403769237060,
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