Dieser Band der Enzyklopädie ist der zweite in der Unterreihe zur Funktionentheorie mehrerer Veränderlicher. Die vier Beiträge des Buches behandeln Themen aus der Potentialtheorie, algebraischen Geometrie, der Funktionentheorie in der Einheitskugel und Twistorgeometrie. Das Buch wird Forschern und Studenten höherer Semester als Nachschlagewerk dienen und sie auch in verschiedene interessante Forschungsgebiete einführen.
This volume of the Encyclopaedia contains four parts each of which being an informative survey of a topic in the field of several complex variables. The first deals with residue theory and its applications to integrals depending on parameters, combinatorial sums and systems of algebraic equations. The second part contains recent results in complex potential theory and the third part treats function theory in the unit ball covering research of the last twenty years. The latter part includes an up-to-date account of research related to a list of problems, which was published by Rudin in 1980. The last part of the book treats complex analysis in the future tube. The future tube is an important concept in mathematical physics, especially in axiomatic quantum field theory, and it is related to Penrose's work on "the complex geometry of the real world". nResearchers and graduate students in complex analysis and mathematical physics will use this book as a reference and as a guide to exciting areas of research.
Contents: Multidimensional Residues and Applications by L.A. Ajzenberg, A.K. Tsikh, A.P. Yuzhakov.- Plurisubharmonic Functions by A. Sadullaev.- Function Theory in the Ball by A.B. Aleksandrov.- Complex Analysis in the Future Tube by A.G. Sergeev and V.S. Vladimirov.