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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.
Added Personal Name	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)
Internet Site	http://dx.doi.org/10.1007/b97238
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Mathematical analysis . Mathematics . Authors: Axler, Sheldon . Bourdon, Paul . Ramey, Wade . Corporate Authors: SpringerLink (Online service) . Series: Graduate texts in mathematics . GTM . Classification: 515 .

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Harmonic Function Theory

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