In this easily-accessible textbook, the authors integrate the ill-posed problem theory and its underlying mathematical apparatus. This comprehensive work includes descriptions of recent results and a presentation of actual applications of the ill-posed problem theory. The first part of the book describes the differentiation of normed space mappings, the integration of the functions of abstract variables, and the theory of linear operators. The second section deals with the mathematical physics connected to integral equations of the first type, and with the bases of operator equation theory.

Comparatively weakly researched untraditional tomography problems aresolved because of new achievements in calculation mathematics and the theory of ill-posed problems, the regularization process of solving ill-posed problems, and the increase of stability. Experiments show possibilities and applicability of algorithms of processing tomography data. This monograph is devoted to considering these problems in connection with series of ill-posed problems in tomography settings arising from practice.The book includes chapters to the following themes:

• Mathematical basis of the...