Capacities in Complex Anaylsis (Aspects of Mathematics): E 14 - Brossura

Cegrell, Urban

Brossura

ISBN 10: 3528063351 ISBN 13: 9783528063351

Casa editrice: Friedrich Vieweg & Sohn Verlagsgesellschaft mbH, 1988

Riassunto

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.

Su questo libro

Contenuti

I. Capacities.- II. Capacitability.- III.a Outer regularity.- III.b Outer regularity (cont.).- IV. Subharmonic functions in ?n.- V. Plurisubharmonic functions in ? n — the Monge-Ampère capacity.- VI. Further properties of the Monge-Ampère operator.- VII. Green’s function.- VIII. The global extremal function.- IX. Gamma capacity.- X. Capacities on the boundary.- XI. Szegö kernels.- XII. Complex homomorphisms.

Dettagli dell'edizione

• Editore: Friedrich Vieweg & Sohn Verlagsgesellschaft mbH
• Data di pubblicazione: 1988
• Lingua: Tedesco
• ISBN 10: 3528063351
• ISBN 13: 9783528063351
• Rilegatura: Copertina flessibile
• Numero di pagine: 172
• Contatto del produttore: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Germania