Capacities in Complex Analysis (Aspects of Mathematics, E 14) (German Edition)

Cegrell, Urban

ISBN 10: 3528063351 / ISBN 13: 9783528063351

Published by Vieweg+Teubner Verlag, 1988

About this Item

LIKE NEW. SHIPS FROM MULTIPLE LOCATIONS.

Seller Inventory # ERICA79035280633516

Bibliographic Details

• Title: Capacities in Complex Analysis (Aspects of Mathematics, E 14) (German Edition)
• Publisher: Vieweg+Teubner Verlag
• Publication Date: 1988
• Language: German
• ISBN 10: 3528063351
• ISBN 13: 9783528063351
• Binding: Paperback
• Condition: Like New
• Book Type: book

About this title

Synopsis

The purpose of this book is to study plurisubharmonic and analytic functions in n using capacity theory. The case n=l has been studied for a long time and is very well understood. The theory has been generalized to mn and the results are in many cases similar to the situation in . However, these results are not so well adapted to complex analysis in several variables - they are more related to harmonic than plurihar- monic functions. Capacities can be thought of as a non-linear generali- zation of measures; capacities are set functions and many of the capacities considered here can be obtained as envelopes of measures. In the mn theory, the link between functions and capa- cities is often the Laplace operator - the corresponding link in the n theory is the complex Monge-Ampere operator. This operator is non-linear (it is n-linear) while the Laplace operator is linear. This explains why the theories in mn and n differ considerably. For example, the sum of two harmonic functions is harmonic, but it can happen that the sum of two plurisubharmonic functions has positive Monge-Ampere mass while each of the two functions has vanishing Monge-Ampere mass. To give an example of similarities and differences, consider the following statements. Assume first that is an open subset VIII of n and that K is a closed subset of Q. Consider the following properties that K mayor may not have.