Invariant potential theory in the unit ball of Cn̳:
This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace–Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson–Szegö integrals on the ball, the Green's function...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1994
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| Schriftenreihe: | London Mathematical Society lecture note series
199 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace–Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson–Szegö integrals on the ball, the Green's function for D and the Riesz decomposition theorem for invariant subharmonic functions. The extension to the ball of the classical Fatou theorem on non-tangible limits of Poisson integrals, and Littlewood's theorem on the existence of radial limits of subharmonic functions are covered in detail. The monograph also contains recent results on admissible and tangential boundary limits of Green potentials, and Lp inequalities for the invariant gradient of Green potentials. Applications of some of the results to Hp spaces, and weighted Bergman and Dirichlet spaces of invariant harmonic functions are included. The notes are self-contained, and should be accessible to anyone with some basic knowledge of several complex variables |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (x, 173 pages) |
| ISBN: | 9780511526183 |
| DOI: | 10.1017/CBO9780511526183 |
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 520 | |a This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace–Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson–Szegö integrals on the ball, the Green's function for D and the Riesz decomposition theorem for invariant subharmonic functions. The extension to the ball of the classical Fatou theorem on non-tangible limits of Poisson integrals, and Littlewood's theorem on the existence of radial limits of subharmonic functions are covered in detail. The monograph also contains recent results on admissible and tangential boundary limits of Green potentials, and Lp inequalities for the invariant gradient of Green potentials. Applications of some of the results to Hp spaces, and weighted Bergman and Dirichlet spaces of invariant harmonic functions are included. The notes are self-contained, and should be accessible to anyone with some basic knowledge of several complex variables | ||
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Datensatz im Suchindex
| _version_ | 1804176883972046848 |
|---|---|
| any_adam_object | |
| author | Stoll, Manfred |
| author_facet | Stoll, Manfred |
| author_role | aut |
| author_sort | Stoll, Manfred |
| author_variant | m s ms |
| building | Verbundindex |
| bvnumber | BV043941798 |
| classification_rvk | SI 320 SK 780 |
| collection | ZDB-20-CBO |
| ctrlnum | (ZDB-20-CBO)CR9780511526183 (OCoLC)967775847 (DE-599)BVBBV043941798 |
| dewey-full | 515.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.9 |
| dewey-search | 515.9 |
| dewey-sort | 3515.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511526183 |
| format | Electronic eBook |
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| id | DE-604.BV043941798 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511526183 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350768 |
| oclc_num | 967775847 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (x, 173 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | London Mathematical Society lecture note series |
| spelling | Stoll, Manfred Verfasser aut Invariant potential theory in the unit ball of Cn̳ Manfred Stoll Cambridge Cambridge University Press 1994 1 online resource (x, 173 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 199 Title from publisher's bibliographic system (viewed on 05 Oct 2015) This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace–Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson–Szegö integrals on the ball, the Green's function for D and the Riesz decomposition theorem for invariant subharmonic functions. The extension to the ball of the classical Fatou theorem on non-tangible limits of Poisson integrals, and Littlewood's theorem on the existence of radial limits of subharmonic functions are covered in detail. The monograph also contains recent results on admissible and tangential boundary limits of Green potentials, and Lp inequalities for the invariant gradient of Green potentials. Applications of some of the results to Hp spaces, and weighted Bergman and Dirichlet spaces of invariant harmonic functions are included. The notes are self-contained, and should be accessible to anyone with some basic knowledge of several complex variables Potential theory (Mathematics) Invariants Unit ball Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Einheitssphäre (DE-588)4151316-2 gnd rswk-swf Einheitssphäre (DE-588)4151316-2 s Mehrere komplexe Variable (DE-588)4169285-8 s Potenzialtheorie (DE-588)4046939-6 s 1\p DE-604 Harmonische Analyse (DE-588)4023453-8 s 2\p DE-604 Erscheint auch als Druckausgabe 978-0-521-46830-5 https://doi.org/10.1017/CBO9780511526183 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Stoll, Manfred Invariant potential theory in the unit ball of Cn̳ Potential theory (Mathematics) Invariants Unit ball Harmonische Analyse (DE-588)4023453-8 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd Potenzialtheorie (DE-588)4046939-6 gnd Einheitssphäre (DE-588)4151316-2 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4169285-8 (DE-588)4046939-6 (DE-588)4151316-2 |
| title | Invariant potential theory in the unit ball of Cn̳ |
| title_auth | Invariant potential theory in the unit ball of Cn̳ |
| title_exact_search | Invariant potential theory in the unit ball of Cn̳ |
| title_full | Invariant potential theory in the unit ball of Cn̳ Manfred Stoll |
| title_fullStr | Invariant potential theory in the unit ball of Cn̳ Manfred Stoll |
| title_full_unstemmed | Invariant potential theory in the unit ball of Cn̳ Manfred Stoll |
| title_short | Invariant potential theory in the unit ball of Cn̳ |
| title_sort | invariant potential theory in the unit ball of cn |
| topic | Potential theory (Mathematics) Invariants Unit ball Harmonische Analyse (DE-588)4023453-8 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd Potenzialtheorie (DE-588)4046939-6 gnd Einheitssphäre (DE-588)4151316-2 gnd |
| topic_facet | Potential theory (Mathematics) Invariants Unit ball Harmonische Analyse Mehrere komplexe Variable Potenzialtheorie Einheitssphäre |
| url | https://doi.org/10.1017/CBO9780511526183 |
| work_keys_str_mv | AT stollmanfred invariantpotentialtheoryintheunitballofcn |