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Capacities in Complex Analysis 1988 Edition
Contributor(s): Cegrell, Urban (Author)

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 ISBN: 3528063351     ISBN-13: 9783528063351
Publisher: Vieweg+teubner Verlag
OUR PRICE: $56.99  

Binding Type: Paperback
Language: German
Published: January 1988
Qty:

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Additional Information
BISAC Categories:
- Computers | Programming - Algorithms
- Mathematics | Functional Analysis
- Mathematics | Mathematical Analysis
Dewey: 515
LCCN: 89103776
Series: Aspects of Mathematics
Physical Information: 0.37" H x 6.14" W x 9.21" L (0.55 lbs) 156 pages
Features: Bibliography
 
Descriptions, Reviews, Etc.
Publisher Description:
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.
 
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