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Potential Theory An Analytic and Probabilistic Approach to Balayage

During the last thirty years potential theory has undergone a rapid development, much of which can still only be found in the original papers. This book deals with one part of this development, and has two aims. The first is to give a comprehensive account of the close connection between analytic an...

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Bibliographic Details
Main Authors: Bliedtner, Jürgen, Hansen, Wolfhard (Author)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1986, 1986
Edition:1st ed. 1986
Series:Universitext
Subjects:
Potential Theory (mathematics)
Potential Theory
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 7. Hunt Processes
  • 8. Four Equivalent Views of Potential Theory
  • V. Examples
  • 1. Subspaces
  • 2. Strong Feller Kernels
  • 3. Subordination by Convolution Semigroups
  • 4. Riesz Potentials
  • 5. Products
  • 6. Heat Equation
  • 7. Brownian Semigroups on the Infinite Dimensional Torus
  • 8. Images
  • 9. Further Examples
  • VI. Balayage Theory
  • 1. Balayage of Functions
  • 2. Balayage of Measures
  • 3. Probabilistic Interpretation
  • 4. Base
  • 5. Exceptional Sets
  • 6. Essential Base
  • 7. Penetration Time
  • 8. Fine Support of Potentials
  • 9. Fine Properties of Balayage
  • 10. Convergence of Balayage Measures
  • 11. Accumulation Points of Balayage Measures
  • 12. Extreme Representing Measures
  • VII. Dirichlet Problem
  • 1. Perron Sets
  • 2. Generalized Dirichlet Problem
  • 3. Regular Points
  • 4. Irregular Points
  • 5. Simplicial Cones
  • 6. Weak Dirichlet Problem
  • 7. Characterization of the Generalized Solution
  • 8. Fine Dirichlet Problem
  • 9. Approximation
  • 0. Classical Potential Theory
  • 1. Harmonic and Hyperharmonic Functions
  • 2. Brownian Semigroup
  • 3. Excessive Functions
  • I. General Preliminaries
  • 1. Function Cones
  • 2. Choquet Boundary
  • 3. Analytic Sets and Capacitances
  • 4. Laplace Transforms
  • 5. Coercive Bilinear Forms
  • II. Excessive Functions
  • 1. Kernels
  • 2. Supermedian Functions
  • 3. Semigroups and Resolvents
  • 4. Balayage Spaces
  • 5. Continuous Potentials
  • 6. Construction of Kernels
  • 7. Construction of Resolvents
  • 8. Construction of Semigroups
  • III. Hyperharmonic Functions
  • 1. Harmonic Kernels
  • 2. Harmonic Structure of a Balayage Space
  • 3. Convergence Properties
  • 4. Minimum Principle and Sheaf Properties
  • 5. Regularizations
  • 6. Potentials
  • 7. Absorbing and Finely Isolated Points
  • 8. Harmonic Spaces
  • IV. Markov Processes
  • 1. Stochastic Processes
  • 2. Markov Processes
  • 3. Transition Functions
  • 4. Modifications
  • 5. Stopping Times
  • 6. Strong Markov Processes
  • 10. Removable Singularities
  • VIII. Partial Differential Equations
  • 1. Bauer Spaces
  • 2. Semi-El1iptic Differential Operators
  • 3. Smooth Bauer Spaces
  • 4. Weak Solutions
  • 5. Elliptic-Parabolic Differential Operators
  • Notes
  • Index of Symbols
  • Guide to Standard Examples

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