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Harmonic Function Theory

Harmonic Function Theory
Catalogue Information
Field name Details
Dewey Class 515
Title Harmonic Function Theory ([EBook] /) / by Sheldon Axler, Paul Bourdon, Wade Ramey.
Author Axler, Sheldon
Added Personal Name Bourdon, Paul author.
Ramey, Wade author.
Other name(s) SpringerLink (Online service)
Publication New York, NY : : Springer New York : : Imprint: Springer, , 1992.
Physical Details XII, 233 p. : online resource.
Series Graduate texts in mathematics 0072-5285 ; ; 137
ISBN 9780387215273
Summary Note 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 behavior. An appendix describes routines for use with MATHEMATICA to manipulate some of the expressions that arise in the study of harmonic functions.:
Contents note 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.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
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