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 Volume, Surface Area, and Integration on Spheres Harmonic Function Theory and Mathematica References Symbol Index Index
* 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 * Volume, Surface Area, and Integration on Spheres * Harmonic Function Theory and Mathematica * References * Symbol Index * Index
This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package supplements the text for readers who wish to explore harmonic function theory on a computer.