This volume is a collection of manscripts mainly originating from talks and lectures given at the Workshop on Recent Trends in Complex Methods for Par- tial Differential Equations held from July 6 to 10, 1998 at the Middle East Technical University in Ankara, Turkey, sponsored by The Scientific and Tech- nical Research Council of Turkey and the Middle East Technical University. This workshop is a continuation oftwo workshops from 1988 and 1993 at the In- ternational Centre for Theoretical Physics in Trieste, Italy entitled Functional analytic Methods in Complex Analysis and Applications to...

Like real analysis, complex analysis has generated methods indispensable to mathematics and its applications. Exploring the interactions between these two branches, this book uses the results of real analysis to lay the foundations of complex analysis and presents a unified structure of mathematical analysis as a whole.

To set the groundwork and mitigate the difficulties newcomers often experience, An Introduction to Complex Analysis begins with a complete review of concepts and methods from real analysis, such as metric spaces and the Green-Gauss Integral Formula. The approach leads to...

Functional analysis is not only a tool for unifying mathematical analysis, but it also provides the background for today's rapid development of the theory of partial differential equations. Using concepts of functional analysis, the field of complex analysis has developed methods (such as the theory of generalized analytic functions) for solving very general classes of partial differential equations. This book is aimed at promoting further interactions of functional analysis, partial differential equations, and complex analysis including its generalizations such as Clifford analysis. New...

An intensive development of the theory of generalized analytic functions started when methods of Complex Analysis were combined with methods of Functional Analysis, especially with the concept of distributional solutions to partial differential equations. The power of these interactions is far from being exhausted. In order to promote the further development of the theory of generalized analytic functions and applications of partial differential equations to Mechanics, the Technical University of Graz organized a conference whose Proceedings are contained in the present volume.
The...

The purpose of the present book is to solve initial value problems in classes of generalized analytic functions as well as to explain the functional-analytic background material in detail. From the point of view of the theory of partial differential equations the book is intend ed to generalize the classicalCauchy-Kovalevskayatheorem, whereas the functional-analytic background connected with the method of successive approximations and the contraction-mapping principle leads to the con cept of so-called scales of Banach spaces: 1. The method of successive approximations allows to solve the...

There is almost no field in Mathematics which does not use Mathe matical Analysis. Computer methods in Applied Mathematics, too, are often based on statements and procedures of Mathematical Analysis. An important part of Mathematical Analysis is Complex Analysis because it has many applications in various branches of Mathematics. Since the field of Complex Analysis and its applications is a focal point in the Vietnamese research programme, the Hanoi University of Technology organized an International Conference on Finite or Infinite Dimensional Complex Analysis and Applications which took...

Dieses Buch stellt eine Einfuhrung in die (komplexe) Funktionentheorie dar. Die Funktionentheorie ist eine nach den verschiedensten Richtungen sehr weit entwickelte mathematische Theorie, deren Grundlage die Theorie der komplexen Differentiation ist. Einer der wichtigsten Satze der Funktionentheorie ist der Cauchysche Integralsatz. Er besagt, dass das komplexe Kurvenintegral einer komplexwertigen Funktion 1 (z) uber eine geschlossene Kurve gleich Null ist, wenn I(z) in jedem Punkt ihres Definitionsgebietes im komplexen Sinne differen zierbar ist. Allerdings gilt diese Aussage nur, wenn uber...