Bücher von Stefan Samko

These proceedings comprise a large part of the papers presented at the In- ternational Conference Factorization, Singular Operators and related problems, which was held from January 28 to February 1, 2002, at the University of th Madeira, Funchal, Portugal, to mark Professor Georgii Litvinchuk's 70 birth- day. Experts in a variety of fields came to this conference to pay tribute to the great achievements of Professor Georgii Litvinchuk in the development of vari- ous areas of operator theory. The main themes of the conference were focussed around the theory of singular type operators and factorization problems, but other topics such as potential theory and fractional calculus, to name but a couple, were also presented. The goal of the conference was to bring together mathematicians from var- ious fields within operator theory and function theory in order to highlight recent advances in problems many of which were originally studied by Profes- sor Litvinchuk and his scientific school. A second aim was to stimulate in- ternational collaboration even further and promote the interaction of different approaches in current research in these areas. The Proceedings will be of great interest to researchers in Operator The- ory, Real and Complex Analysis, Functional and Harmonic Analysis, Potential Theory, Fractional Calculus and other areas, as well as to graduate students looking for the latest results.

Equations with Involutive Operators demonstrates an important interplay between abstract and concrete operator theory. The focus is on the investigation of a number of equations, which, while seemingly different, are all unified by the same idea: they are all realizations of some operator equations in Banach spaces. One permeating theme in these equations involves the role of the Fredholm property. The text is carefully written, self-contained, and covers a broad range of topics and results. Key ideas are developed in a step-by step approach, beginning with required background and historical material, and culminating in the final chapters with state-of-the art topics. Experts in operator theory, integral equations, and function theory as well as students in these areas will find open problems for further investigations. The book will also be useful to engineers using operator theory and integral equation techniques. Good examples, bibliography and index make this text a valuable classroom or reference resource.

This volume presents a comprehensive treatment of hypersingular integrals and their applications. Hypersingular integrals arise as constructions inverse to potential type operators and are realised by these approaches: method of regularization; method of finite differences.