First-kind equations on a sphere and some problems of convex geometry
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| 024 | 7 | 0 | |a 10.1515/156939403769237060 |2 doi |
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| 100 | 1 | |a Stepanov |D V. N. |u Omsk State Technical University. E-Mail: stepaw49@rol.ru | |
| 245 | 1 | 0 | |a First-kind equations on a sphere and some problems of convex geometry |h [Elektronische Daten] |c [V. N. Stepanov] |
| 520 | 3 | |a 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. | |
| 540 | |a Copyright 2003, Walter de Gruyter | ||
| 773 | 0 | |t Journal of Inverse and Ill-posed Problems |d Walter de Gruyter |g 11/3(2003-09-01), 289-310 |x 0928-0219 |q 11:3<289 |1 2003 |2 11 |o jiip | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/156939403769237060 |q text/html |z Onlinezugriff via DOI |
| 908 | |D 1 |a research article |2 jats | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1515/156939403769237060 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Stepanov |D V. N. |u Omsk State Technical University. E-Mail: stepaw49@rol.ru | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Journal of Inverse and Ill-posed Problems |d Walter de Gruyter |g 11/3(2003-09-01), 289-310 |x 0928-0219 |q 11:3<289 |1 2003 |2 11 |o jiip | ||
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| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-gruyter | ||