Several Complex Variables: Function Theory in Classical Domains Complex Potential Theory

This volume of the Encyclopaedia contains four parts each ofwhich being an informative survey of a topic in the field ofseveral complex variables. Thefirst deals with residuetheory and its applications to integrals depending onparameters, combinatorial sums and systems of algebraicequations. The second part contains recent results incomplex potential theory and the third part treats functiontheory in the unit ball covering research of the last twentyyears. The latter part includes an up-to-date account ofresearch related to a list of problems, which was publishedby Rudin in 1980. The last part of the book treats complex analysis in thefuturetube. The future tube is an important concept inmathematical physics, especially in axiomatic quantum fieldtheory, and it is related to Penrose'swork on "the complexgeometry of the real world". Researchers and graduate students in complex analysis andmathematical physics will use thisbook as a reference andas a guide to exciting areas of research.