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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Capacities in Complex Analysis

Capacities in Complex Analysis

Cegrell, Urban

Paperback

Series: Aspects of Mathematics, Book 14

General MathematicsProgramming

ISBN10: 3528063351
ISBN13: 9783528063351
Publisher: Springer Nature
Published: Jan 1 1988
Pages: 156
Weight: 0.55
Height: 0.37 Width: 6.14 Depth: 9.21
Language: German
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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