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Harmonic Function Theory

Harmonic Function Theory
Catalogue Information
Field name Details
Dewey Class 515.96
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)
Edition statement Second Edition.
Publication New York, NY : : Springer New York : : Imprint: Springer, , 2001.
Physical Details XII, 264 p. : online resource.
Series Graduate texts in mathematics 0072-5285 ; ; 137
ISBN 9781475781373
Summary Note This is a book about harmonic functions in Euclidean space. Readers with a background in real and complex analysis at the beginning graduate level will feel comfortable with the material presented here. The authors have taken unusual care to motivate concepts and simplify proofs. Topics include: basic properties of harmonic functions, Poisson integrals, the Kelvin transform, spherical harmonics, harmonic Hardy spaces, harmonic Bergman spaces, the decomposition theorem, Laurent expansions, isolated singularities, and the Dirichlet problem. The new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bocher's Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package-designed by the authors and available by e-mail - supplements the text for readers who wish to explore harmonic function theory on a computer.:
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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