Harmonic Function Theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1992
|
| Schriftenreihe: | Graduate Texts in Mathematics
137 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XII, 233 p) |
| ISBN: | 9780387215273 9781489911865 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/b97238 |
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| 500 | |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 | ||
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/b97238 |
| format | Electronic eBook |
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| id | DE-604.BV042418906 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:03Z |
| institution | BVB |
| isbn | 9780387215273 9781489911865 |
| issn | 0072-5285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027854323 |
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| physical | 1 Online-Ressource (XII, 233 p) |
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| publishDate | 1992 |
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| publisher | Springer New York |
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| series2 | Graduate Texts in Mathematics |
| spelling | Axler, Sheldon Verfasser aut Harmonic Function Theory by Sheldon Axler, Paul Bourdon, Wade Ramey New York, NY Springer New York 1992 1 Online-Ressource (XII, 233 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 137 0072-5285 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 Mathematics Global analysis (Mathematics) Analysis Mathematik Harmonische Funktion (DE-588)4159122-7 gnd rswk-swf Harmonische Funktion (DE-588)4159122-7 s 1\p DE-604 Bourdon, Paul Sonstige oth Ramey, Wade Sonstige oth https://doi.org/10.1007/b97238 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Axler, Sheldon Harmonic Function Theory Mathematics Global analysis (Mathematics) Analysis Mathematik Harmonische Funktion (DE-588)4159122-7 gnd |
| subject_GND | (DE-588)4159122-7 |
| title | Harmonic Function Theory |
| title_auth | Harmonic Function Theory |
| title_exact_search | Harmonic Function Theory |
| title_full | Harmonic Function Theory by Sheldon Axler, Paul Bourdon, Wade Ramey |
| title_fullStr | Harmonic Function Theory by Sheldon Axler, Paul Bourdon, Wade Ramey |
| title_full_unstemmed | Harmonic Function Theory by Sheldon Axler, Paul Bourdon, Wade Ramey |
| title_short | Harmonic Function Theory |
| title_sort | harmonic function theory |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Harmonische Funktion (DE-588)4159122-7 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Harmonische Funktion |
| url | https://doi.org/10.1007/b97238 |
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