Description
Book SynopsisBasic 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.
Trade ReviewFrom the reviews of the second edition:
"There are several major changes in this second edition … . Many exercises have been added and several photographs of mathematicians related to harmonic functions are included. The book is a nice introduction to the fundamental notions of potential theory." (European Mathematical Society Newsletter, June, 2002)
"We warmly recommend this textbook to graduate students interested in Harmonic Function Theory and/or related areas. We are sure that the reader will be able to appreciate the lively and illuminating discussions in this book, and therefore, will certainly gain a better understanding of the subject." (Ferenc Móricz, Acta Scientiarum Mathematicarum, Vol. 67, 2001)
"This is a new edition of a nice textbook … on harmonic functions in Euclidean spaces, suitable for a beginning graduate level course. … New exercises are added and numerous minor improvements throughout the text are made." (Alexander Yu. Rashkovsky, Zentralblatt MATH, Vol. 959, 2001)
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 * Volume, Surface Area, and Integration on Spheres * Harmonic Function Theory and Mathematica * References * Symbol Index * Index
