TU Chemnitz: Fakultät für Mathematik: Professur für Wirtschaftsmathematik

This book is the first part of an introduction into the theory of linear one-dimensional singular integral operators. The main topics of this volume are: boundedness of singular integral operators in various function spaces, invertibility of these operators, and inversion methods, Noether-Fredholm theory, and local principles.

The book contains both a general abstract approach and concrete solution methods for singular integral equations, various applications, numerous examples and exercises. Here only singular integral operators with continuous coefficients on closed curves are considered. The case of discontinuous coefficients and more general curves will be considered in a second volume.

The exposition is self-contained and has been polished in an effort to make the book accessible to a wide audience of students and researchers in mathematics, science and engineering.

• The Operator of Singular Integration
• One-sided Invertible Operators
• Singular Integral Operators with Continuous Coefficients
• Fredholm Operators
• Local Principles and their first Applications