Volterra Equations and Inverse Problems (Inverse and III-Posed Problems)

This text deals with the theory of multidimensional Volterra equations and their applications to multidimensional inverse problems. The book opens with the basic concepts of the general ill-posed problem theory, followed by elements of the abstract operator Volterra theory. Subsequent chapters deal with: linear and nonlinear operator equations in scales of Banach spaces and applications to inverse problems; investigations by the method of the weight a priori estimates and the method based on the spectral von Neumann theorem; multidimensional integro-differential Volterra equations and problems of integral geometry; and inverse problems of wave scattering and propagation.