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MARC 21

Harmonic Function Theory
Tag	Description
020	$a9780387215273$9978-0-387-21527-3
082	$a515$223
099	$aOnline resource: Springer
100	$aAxler, Sheldon.
245	$aHarmonic Function Theory$h[EBook] /$cby Sheldon Axler, Paul Bourdon, Wade Ramey.
260	$aNew York, NY :$bSpringer New York :$bImprint: Springer,$c1992.
300	$aXII, 233 p.$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	$aHarmonic 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.
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/b97238