Harmonic Function Theory

• Main Authors: Axler, Sheldon. (Author), Bourdon, Paul. (Author), Ramey, Wade. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 1992.
• Series: Graduate Texts in Mathematics, 137
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Analysis.
• Online Access: View fulltext via EzAccess

Harmonic functions - the solutions of Laplace's equation - play a crucial role in many areas of mathematics, physics, and engineering. Avoiding the disorganization and inconsistent notation of other expositions, the authors approach the field from a more function-theoretic perspective, emphasiz...

Table of Contents:

• Basic Properties of Harmonic Functions
• Bounded Harmonic Functions
• Positive Harmonic Functions
• The Kelvin Transform
• Harmonic Polynomials
• Harmonic Hardy Spaces
• Harmonic Functions on Half-Spaces
• Harmonic Bergman Spaces
• The Decomposition Theorem
• Annular Regions
• The Dirichlet Problem and Boundary Behavior.