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Capacities in Complex Analysis

By Urban Cegrell

Capacities in Complex Analysis Computer Science

Capacities in Complex Analysis

By Urban Cegrell

0 - Default Title
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.
Product details
Binding:
Paperback
Edition:
1
Number of Pages:
172
Release Date:
1988-01-01
Publication Date:
1988-01-01
Publisher:
Vieweg+Teubner Verlag
Languages:
Original: German
ISBN10:
3528063351
ISBN13:
9783528063351
GPSR Manufacturer Reference:
[email protected]
Weight:
271 g
Height:
155 cm
Width:
235 cm
Thickness:
10 cm
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