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 8
• 2 System of Volterra integral equations of the first kind 14
• 2.1 The system of Volterra linear integral equations of the first kind in the interval 14
• 2.2 Stability of solutions of Volterra integral equations of the second kind in the semiaxis 37
• 2.3 The system of Volterra integral equations of the first kind in the semiaxis 47
• 2.4 The system of Volterra linear integral equations of the first kind in the space of square-integrable functions 60
• 3 The system of Volterra linear integral equations of the first kind of the convolution type and the commutative ring 70
• 3.1 The system of Volterra integral equations of the first kind of the convolution type 70
• 3.2 Commutative ring and a system of equations in it 91
• 3.3 Application to inverse problems 114
• 4.1 The system of two-dimensional Volterra linear integral equations of the first kind 118
• 4 The system of Volterra integral equations of the first kind with two independent variables 118
• 4.2 The system of Volterra nonlinear two-dimensional integral equations of the first kind 137
• 5.1 Volterra operator equations of the first kind in the scales of Hilbert spaces 148
• 5 Volterra operator equations 148