Irregular Equations As Ill–Posed Problems

The aim of this chapter is to introduce necessary mathematical background for the succeeding exposition. For the reader’s convenience, in Section 1.1 we collect frequently used facts concerning theory of linear operators and nonlinear analysis. In Section 1.2 we sketch the basics of contemporary theory of ill–posed problems. We recall fundamental notions of this theory such as regularization algorithm and regularization parameter. We also discuss interrelations between these notions and main ideas of the book.