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MARC 21

Harmonic Function Theory
Tag	Description
020	$a9781475781373$9978-1-4757-8137-3
082	$a515.96$223
099	$aOnline resource: Springer
100	$aAxler, Sheldon.
245	$aHarmonic Function Theory$h[EBook] /$cby Sheldon Axler, Paul Bourdon, Wade Ramey.
250	$aSecond Edition.
260	$aNew York, NY :$bSpringer New York :$bImprint: Springer,$c2001.
300	$aXII, 264 p.$bonline resource.
336	$atext$btxt$2rdacontent
337	$acomputer$bc$2rdamedia
338	$aonline resource$bcr$2rdacarrier
440	$aGraduate Texts in Mathematics,$x0072-5285 ;$v137
505	$aBasic 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.
520	$aThis 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.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
700	$aBourdon, Paul.$eauthor.
700	$aRamey, Wade.$eauthor.
710	$aSpringerLink (Online service)
830	$aGraduate Texts in Mathematics,$x0072-5285 ;$v137
856	$uhttp://dx.doi.org/10.1007/978-1-4757-8137-3