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...

Plurisubharmonic functions playa major role in the theory of functions of several complex variables. The extensiveness of plurisubharmonic functions, the simplicity of their definition together with the richness of their properties and. most importantly, their close connection with holomorphic functions have assured plurisubharmonic functions a lasting place in multidimensional complex analysis. (Pluri)subharmonic functions first made their appearance in the works of Hartogs at the beginning of the century. They figure in an essential way, for example, in the proof of the famous theorem of...