Harmonic Function Theory (Graduate Texts in Mathematics)

Bourdon, Paul S.; Axler, Sheldon; Ramey, Wade; Ramey, W.

ISBN 10: 3540978755 / ISBN 13: 9783540978756

Verlag: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1992

Beschreibung

Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher.

Bestandsnummer des Verkäufers 41822728/202

Bibliografische Details

• Titel: Harmonic Function Theory (Graduate Texts in Mathematics)
• Verlag: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Erscheinungsjahr: 1992
• Sprache: Englisch
• ISBN-10: 3540978755
• ISBN-13: 9783540978756
• Einband: Hardcover
• Zustand: Sehr gut
• Verkäuferkataloge:
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Über diesen Titel

Inhaltsangabe

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.