|
|
|
|
| LEADER |
02418nmm a2200301 u 4500 |
| 001 |
EB000614630 |
| 003 |
EBX01000000000000000467712 |
| 005 |
00000000000000.0 |
| 007 |
cr||||||||||||||||||||| |
| 008 |
140122 ||| eng |
| 020 |
|
|
|a 9780387215273
|
| 100 |
1 |
|
|a Axler, Sheldon
|
| 245 |
0 |
0 |
|a Harmonic Function Theory
|h Elektronische Ressource
|c by Sheldon Axler, Paul Bourdon, Wade Ramey
|
| 250 |
|
|
|a 1st ed. 1992
|
| 260 |
|
|
|a New York, NY
|b Springer New York
|c 1992, 1992
|
| 300 |
|
|
|a XII, 233 p
|b online resource
|
| 505 |
0 |
|
|a 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
|
| 653 |
|
|
|a Mathematical analysis
|
| 653 |
|
|
|a Analysis
|
| 700 |
1 |
|
|a Bourdon, Paul
|e [author]
|
| 700 |
1 |
|
|a Ramey, Wade
|e [author]
|
| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
|
| 989 |
|
|
|b SBA
|a Springer Book Archives -2004
|
| 490 |
0 |
|
|a Graduate Texts in Mathematics
|
| 028 |
5 |
0 |
|a 10.1007/b97238
|
| 856 |
4 |
0 |
|u https://doi.org/10.1007/b97238?nosfx=y
|x Verlag
|3 Volltext
|
| 082 |
0 |
|
|a 515
|
| 520 |
|
|
|a 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
|