Abstract
In this chapter, we study the question of reducing the problem of integral geometry for a special class of surfaces to the Cauchy problem for some equation of evolutionary type. Fourier transform methods are also used. Methods are obtained that allow reducing the problem of integral geometry for special families of curves and surfaces to the Cauchy problem for equations of evolutionary type, and classes of such problems are distinguished. Uniqueness theorems are proved for some new classes of operator equations of Voltaire type in three-dimensional space.
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