Potential analysis of stable processes and its extensions /
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| Imprint: | Berlin : Springer, c2009. |
|---|---|
| Description: | ix, 187 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | Lecture notes in mathematics ; 1980 Lecture notes in mathematics (Springer-Verlag) ; 1980. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/7805335 |
Table of Contents:
- 1. Introduction
- 1.1. Bases of Potential Theory of Stable Processes
- 1.1.1. Classical Potential Theory
- 1.1.2. Potential Theory of the Riesz Kernel
- 1.1.3. Green Function and Poisson Kernel of &Delta ¿/2
- 1.1.4. Subordinate Brownian Motions
- 1.2. Outline of the Book
- 2. Boundary Potential Theory for Schrödinger Operators Based on Fractional Laplacian
- 2.1. Introduction
- 2.2. Boundary Harnack Principle
- 2.3. Approximate Factorization of Green Function
- 2.4. Schrodinger Operator and Conditional Gauge Theorem
- 3. Nontangential Convergence for ¿-harmonic Functions
- 3.1. Introduction
- 3.2. Basic Definitions and Properties
- 3.3. Relative Fatou Theorem for ¿-Harmonic Functions
- 3.4. Extensions to Other Processes
- 4. Eigenvalues and Eigenfunctions for Stable Processes
- 4.1. Introduction
- 4.2. Intrinsic Ultracontractivity (IU)
- 4.3. Steklov Problem
- 4.4. Eigenvalue Estimates
- 4.5. Generalized Isoperimetric Inequalities
- 5. Potential Theory of Subordinate Brownian Motion
- 5.1. Introduction
- 5.2. Subordinators
- 5.2.1. Special Subordinators and Complete Bernstein Functions
- 5.2.2. Examples of Subordinators
- 5.2.3. Asymptotic Behavior of the Potential, Lévy and Transition Densities
- 5.3. Subordinate Brownian Motion
- 5.3.1. Definitions and Technical Lemma
- 5.3.2. Asymptotic Behavior of the Green Function
- 5.3.3. Asymptotic Behavior of the Jumping Function
- 5.3.4. Transition Densities of Symmetric Geometric Stable Processes
- 5.4. Harnack Inequality for Subordinate Brownian Motion
- 5.4.1. Capacity and Exit Time Estimates for Some Symmetric Lévy Processes
- 5.4.2. Krylov-Safonov-type Estimate
- 5.4.3. Proof of Harnack Inequality
- 5.5. Subordinate Killed Brownian Motion
- 5.5.1. Definitions
- 5.5.2. Representation of Excessive and Harmonic Functions of Subordinate Process
- 5.5.3. Harnack Inequality for Subordinate Process
- 5.5.4. Martin Boundary of Subordinate Process
- 5.5.5. Boundary Harnack Principle for Subordinate Process
- 5.5.6. Sharp Bounds for the Green Function and the Jumping Function of Subordinate Process
- Bibliography
- Index
