Some New Classes Ill-Posed Problems of Integral Geometry

This preprint presents some new classes ill-posed problems of integral geometry. The paper deals with weakly ill-posed problems of integral geometry of Volterra type associated with integration over curves having a singularity at the vertex, as well as over parabolas and paraboloids with weight functions of a special form. A uniqueness theorem is proved, and stability estimates of the solution in spaces of finite smoothness are obtained. Inversion formulas are derived. Preprint No. 40.Russian Academy of Sciences, Siberian Branch, Institute of Mathematics.1997. 30 pages.References: 17.

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