The aim of the book is to propose a new algebraic approach to the study of norm stability of operator sequences which arise in singular integral equations on composed curves. It is concerned with the different kinds of invertibility of convolution operators.
The authors start with summarizing some necessary facts from operator theory and analyze the so-called finite section method for Toeplitz operators with continuous generating function. Next, they introduce and investigate a comprehensive Banach algebra of approximation sequences. Complete necessary and sufficient conditions for the stability of the involved sequences are derived. This algebra is extended by including certain cutting-off-sequences. Then necessary and sufficient conditions for the stability of the modified spline projection methods are derived.
The above results are employed for approximation methods for singular integral operators on arbitrary Lyapunov curves.