Potential Theory An Analytic and Probabilistic Approach to Balayage

Potential Theory An Analytic and Probabilistic Approach to Balayage / by Jürgen Bliedtner, Wolfhard Hansen.

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 (Author), Hansen, Wolfhard (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1986.
Edition:1st ed. 1986.
Series:Universitext,
Springer eBook Collection.
Subjects:
Potential theory (Mathematics).
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 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
  • 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
  • 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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