Author | Bliedtner, Jรผrgen. author |
---|---|
Title | Potential Theory [electronic resource] : An Analytic and Probabilistic Approach to Balayage / by Jรผrgen Bliedtner, Wolfhard Hansen |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1986 |
Connect to | http://dx.doi.org/10.1007/978-3-642-71131-2 |
Descript | XIII, 435p. online resource |
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