Pluripotential Theory

ISBN-13: 9780198535683 / Angielski / Twarda / 1992 / 288 str.

Klimek, Maciej

Opis

Pluripotential theory is a recently developed non-linear complex counterpart of classical potential theory. Its main area of application is multidimensional complex analysis. The central part of the pluripotential theory is occupied by maximal plurisubharmonic functions and the generalized complex Monge-Ampere operator. The interplay between these two concepts provides the focal point of this monograph, which contains an up-to-date account of the developments from the large volume of recent work in this area. A substantial proportion of the work is devoted to classical properties of subharmonic and plurisubharmonic functions, which makes the pluripotential theory available for the first time to a wide audience of analysts.

Recenzje

'This monograph will surely become a standard work both for mathematicians wishing to learn about pluripotential theory and for those who are already actively researching in this field.' D.H. Armitage, Zentralblatt für Mathematik und ihre Grenzgebiete Mathematics Abstracts

Spis treści

PART I: Complex Differentiation; Subharmonic and plurisubharmonic functions; PART II: The Complex Monge-Ampere Operator: The Dirichet problem for the Monge-Ampere operator; Maximal functions of logarithmic growth; Maximal functions with logarithmic singularities; Appendix: foliations, references; Index.