Harmonic function theory. Graduate Texts in Mathematics; 137.

Axler, Sheldon Jay:

ISBN 10: 3540978755 / ISBN 13: 9783540978756

Published by New York, Springer, 1992

About this Item

XII, 231 p. Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. C-05173 3540978755 Sprache: Englisch Gewicht in Gramm: 550. Seller Inventory # 2491421

Bibliographic Details

Title: Harmonic function theory. Graduate Texts in ...

Publisher: New York, Springer

Publication Date: 1992

Binding: Hardcover

About this title

Synopsis:

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, emphasizing techniques and results that will seem natural to mathematicians comfortable with complex function theory and harmonic analysis; prerequisites for the book are a solid foundation in real and complex analysis together with some basic results from functional analysis. Topics covered include: basic properties of harmonic functions defined on subsets of Rn, including Poisson integrals; properties bounded functions and positive functions, including Liouville's and Cauchy's theorems; the Kelvin transform; Spherical harmonics; hp theory on the unit ball and on half-spaces; harmonic Bergman spaces; the decomposition theorem; laurent expansions and classification of isolated singularities; and boundary behaviour. An appendix describes routines for use with "Mathematica" to manipulate some of the expressions that arise in the study of harmonic functions.

Review:

From 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)