Regularization, Uniqueness And Existence Of Solutions Of Volterra Equations Of The First Kind (inverse And Ill-posed Problems)

The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology. 1 Introduction 2 System of Volterra integral equations of the first kind 2.1 The system of Volterra linear integral equations of the first kind in the interval 2.2 Stability of solutions of Volterra integral equations of the second kind in the semiaxis 2.3 The system of Volterra integral equations of the first kind in the semiaxis 2.4 The system of Volterra linear integral equations of the first kind in the space of square-integrable functions 3 The system of Volterra linear integral equations of the first kind of the convolution type and the commutative ring 3.1 The system of Volterra integral equations of the first kind of the convolution type 3.2 Commutative ring and a system of equations in it 3.3 Application to inverse problems 4 The system of Volterra integral equations of the first kind with two independent variables 4.1 The system of two-dimensional Volterra linear integral equations of the first kind 4.2 The system of Volterra nonlinear two-dimensional integral equations of the first kind 5 Volterra operator equations 5.1 Volterra operator equations of the first kind in the scales of Hilbert spaces 5.2 Volterra operator equations of the first kind in the scales of Banach spaces 5.3 Volterra operator equations of the first kind with commuting kernels 5.4 On uniqueness of solution of Volterra operator equations 5.5 Nonlinear Volterra operator equations of the first kind 6 Problems of integral geometry 6.1 The problem of integral geometry in the three dimensional band 6.2 The problem of integral geometry in a two-dimensional band 6.3 The problem of integral geometry with spatial curves 6.4 The equations connected with problems of integral geometry 7 Bibliography This monograph deals with the problems of regularization, uniqueness and existence of solutions of Volterra integral and operator equations of the first kind with kernels, which are nondifferentiable and irreversible in the diagonal.