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Weakly ill-posed problems of integral geometry witch perturbation on polygonal lines. (Russian. English summary) Zbl 1326.45006

Summary: We study a 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. Using these representations 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.

MSC:

45J05 Integro-ordinary differential equations
35A22 Transform methods (e.g., integral transforms) applied to PDEs
44A15 Special integral transforms (Legendre, Hilbert, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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