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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year

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Rank 59 out of 312 in category Mathematics and 93 out of 254 in Applied Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition

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Volume 11, Issue 3 (Sep 2003)


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

V. N. Stepanov

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.

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Published in Print: 2003-09-01

Citation Information: Journal of Inverse and Ill-posed Problems jiip, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/156939403769237060. Export Citation

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