Title: Introduction to the Theory of Singular Integral Operators with Shift
Description: This book is devoted to the Fredholm theory of singular integral operators with shift in Lp, 1<p<INFINITY spaces. Fredholm criteria are derived and the indices of the Fredholm operators are computed. Simultaneously, a theory of continuous invertibility for functional operators is constructed, and its relation to the theory of dynamical systems is discussed. Also, a new systematic approach to the Fredholm theory of classical singular integral equations with Cauchy kernel is proposed. Detailed proofs are given throughout. The book contains an extensive survey of the literature on closely related topics. This book is of interest to graduate students and mathematicians. The book is self-contained and can be used as a main reference for special course seminars on singular integral operators.
Subjects: Functions of complex variables, Special Functions, Operator theory, Integral equations, Mathematics, Functional equations, Functions, special, Difference and Functional Equations