Complex Potential Theory
Gert Sabidussi, Paul M. Gauthier, "Complex Potential Theory"
English | 1994 | ISBN: 0792330056, 9401044031 | DJVU | pages: 576 | 5.0 mb
English | 1994 | ISBN: 0792330056, 9401044031 | DJVU | pages: 576 | 5.0 mb
In Complex Potential Theory, specialists in several complex variables meet with specialists in potential theory to demonstrate the interface and interconnections between their two fields. The following topics are discussed:
- Real and complex potential theory. Capacity and approximation, basic properties of plurisubharmonic functions and methods to manipulate their singularities and study theory growth, Green functions, Chebyshev-like quadratures, electrostatic fields and potentials, propagation of smallness.
- Complex dynamics. Review of complex dynamics in one variable, Julia sets, Fatou sets, background in several variables, Hénon maps, ergodicity use of potential theory and multifunctions.
- Banach algebras and infinite dimensional holomorphy. Analytic multifunctions, spectral theory, analytic functions on a Banach space, semigroups of holomorphic isometries, Pick interpolation on uniform algebras and von Neumann inequalities for operators on a Hilbert space.