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Harmonic function theory

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: bas...

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Detalles Bibliográficos
Autores principales: Axler, Sheldon, Bourdon, Paul, Ramey, Wade
Lenguaje:eng
Publicado: Springer 2013
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-1-4757-8137-3
http://cds.cern.ch/record/1667047
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author Axler, Sheldon
Bourdon, Paul
Ramey, Wade
author_facet Axler, Sheldon
Bourdon, Paul
Ramey, Wade
author_sort Axler, Sheldon
collection CERN
description 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.
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spelling cern-16670472021-04-21T21:15:38Zdoi:10.1007/978-1-4757-8137-3http://cds.cern.ch/record/1667047engAxler, SheldonBourdon, PaulRamey, WadeHarmonic function theoryMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:16670472013
spellingShingle Mathematical Physics and Mathematics
Axler, Sheldon
Bourdon, Paul
Ramey, Wade
Harmonic function theory
title Harmonic function theory
title_full Harmonic function theory
title_fullStr Harmonic function theory
title_full_unstemmed Harmonic function theory
title_short Harmonic function theory
title_sort harmonic function theory
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-1-4757-8137-3
http://cds.cern.ch/record/1667047
work_keys_str_mv AT axlersheldon harmonicfunctiontheory
AT bourdonpaul harmonicfunctiontheory
AT rameywade harmonicfunctiontheory