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The Problem of Integral Geometry of Volterra Type with a Weight Function of a Special Typeстатья
- Авторы: Begmatov Akram H., Muminov M.E., Ochilov Z.H.
- Журнал: Mathematics the Operations for sgh. and Statistics, ser. Statistics
- Год издания: 2015
- Первая страница: 113
- Последняя страница: 120
- DOI: 10.13189/ms.2015.030501
- Аннотация: We study new problem of reconstruction of a function in a strip from their given integrals with known weight function along polygonal lines. We obtained two simply inversion formulas for the solution to the problem. We prove uniqueness and existence theorems for solutions and obtain stability estimates of a solution to the problem in Sobolev's spaces and thus show their weak ill-posedness. Then we consider integral geometry problems with perturbation. The uniqueness theorems are proved and stability estimates of solutions in Sobolev spaces are obtained. KEYWORDS Ill-posed Problems, Integral Geometry Problems, Integral Transforms, Inversion Formula, Uniqueness, Existence Theorem, Weak Instability, Perturbation
- Добавил в систему: Begmatov Akram Xasanovich