Analytic and plurisubharmonic functions: in finite and infinite dimensional spaces ; course given at the University of Maryland, spring 1970
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1971
|
| Series: | Lecture notes in mathematics
198 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 90 S. |
| ISBN: | 3540054723 0387054723 |
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| 245 | 1 | 0 | |a Analytic and plurisubharmonic functions |b in finite and infinite dimensional spaces ; course given at the University of Maryland, spring 1970 |c Michel Hervé |
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| 490 | 1 | |a Lecture notes in mathematics |v 198 | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Chapter I. Classical potential theory 1
§1. Harmonic functions 1
1.1. The class H(U) of harmonic functions 1
1.2. Harmonic distributions 3
1.3. The Poisson kernel i+
§2. Hyper-, super-, nearly super-harmonic functions 6
2.1. Hyperharmonic functions 6
2.2. The class S(U) of superharmonic functions 8
2.3. Superharmonic distributions and Newton potentials 11
2.4. The class NiV) of nearly superharmonic functions 13
§3. Sweeping-out theory, polar sets and quasisuperharmonic
functions 17
3.1. Sweeping-out 17
3.2. Choquet capacities related to the sweeping-out
process 19
3.3. Polar sets 23
3.4. The class Q_(U) of quasisuperharmonic functions 26
References for Chapter I 30
Chapter II. Plurisuperharmonicity and separate analyticity
with respect to a finite number of variables 31
§1. Plurihyperharmonic and separately hyperharmonic functions 31
1.1. Separately hyperharmonic functions 31
1.2. Plurihyperharmonic and plurisuperharmonic functions 35
1.3. The class WP(fl) of nearly plurisuperharmonic
functions 37
§2. Separate analyticity 41
2.1. Hartogs theorems for the complex case 41
VI
2.2. Siciak s theorem for the real case 44
2.3. The real case: proofs of Propositions 1 and 2 stated
in the preceding section 48
2.4. Lelong s theorem for the harmonic case 53
References for Chapter II 54
Chapter III. Complex analysis in infinite dimensional vector
spaces 56
§1. Analytic maps in the sense of Gateaux 56
1.1. Topological vector spaces 56
1.2. Analytic maps defined on finite dimensional open sets 58
1.3. The class G(U,Y) of Gateaux-analytic maps 65
1.4. Plurihyperharmonic functions 71
§2. Analytic maps in the sense of Frechet 73
2.1. Some criteria for the continuity of a Gateaux-
analytic map 73
2.2. The class A(.U,Y) of analytic maps 76
2.3. A deeper investigation of A(.X, £.) 82
2.4. The class P(P.) of plurisuperharmonic functions 87
References for Chapter III 90
|
| any_adam_object | 1 |
| author | Hervé, Michel 1921-2011 |
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| building | Verbundindex |
| bvnumber | BV002965327 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA3 |
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| callnumber-sort | QA 13 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 |
| ctrlnum | (OCoLC)889242464 (DE-599)BVBBV002965327 |
| dewey-full | 515/.53 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.53 |
| dewey-search | 515/.53 |
| dewey-sort | 3515 253 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | Pluriharmonische Funktion gnd |
| genre_facet | Pluriharmonische Funktion |
| id | DE-604.BV002965327 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:51:31Z |
| institution | BVB |
| isbn | 3540054723 0387054723 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001856589 |
| oclc_num | 889242464 |
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| physical | VI, 90 S. |
| psigel | HUB-ZB011200909 |
| publishDate | 1971 |
| publishDateSearch | 1971 |
| publishDateSort | 1971 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Hervé, Michel 1921-2011 Verfasser (DE-588)1036382966 aut Analytic and plurisubharmonic functions in finite and infinite dimensional spaces ; course given at the University of Maryland, spring 1970 Michel Hervé Berlin [u.a.] Springer 1971 VI, 90 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 198 Fonctions analytiques Fonctions harmoniques Analytic functions Plurisubharmonic functions Plurisubharmonische Funktion (DE-588)4174927-3 gnd rswk-swf Analytische Funktion (DE-588)4142348-3 gnd rswk-swf Pluriharmonische Funktion gnd rswk-swf Plurisubharmonische Funktion (DE-588)4174927-3 s DE-604 Analytische Funktion (DE-588)4142348-3 s Pluriharmonische Funktion f Lecture notes in mathematics 198 (DE-604)BV000676446 198 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001856589&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hervé, Michel 1921-2011 Analytic and plurisubharmonic functions in finite and infinite dimensional spaces ; course given at the University of Maryland, spring 1970 Lecture notes in mathematics Fonctions analytiques Fonctions harmoniques Analytic functions Plurisubharmonic functions Plurisubharmonische Funktion (DE-588)4174927-3 gnd Analytische Funktion (DE-588)4142348-3 gnd |
| subject_GND | (DE-588)4174927-3 (DE-588)4142348-3 |
| title | Analytic and plurisubharmonic functions in finite and infinite dimensional spaces ; course given at the University of Maryland, spring 1970 |
| title_auth | Analytic and plurisubharmonic functions in finite and infinite dimensional spaces ; course given at the University of Maryland, spring 1970 |
| title_exact_search | Analytic and plurisubharmonic functions in finite and infinite dimensional spaces ; course given at the University of Maryland, spring 1970 |
| title_full | Analytic and plurisubharmonic functions in finite and infinite dimensional spaces ; course given at the University of Maryland, spring 1970 Michel Hervé |
| title_fullStr | Analytic and plurisubharmonic functions in finite and infinite dimensional spaces ; course given at the University of Maryland, spring 1970 Michel Hervé |
| title_full_unstemmed | Analytic and plurisubharmonic functions in finite and infinite dimensional spaces ; course given at the University of Maryland, spring 1970 Michel Hervé |
| title_short | Analytic and plurisubharmonic functions |
| title_sort | analytic and plurisubharmonic functions in finite and infinite dimensional spaces course given at the university of maryland spring 1970 |
| title_sub | in finite and infinite dimensional spaces ; course given at the University of Maryland, spring 1970 |
| topic | Fonctions analytiques Fonctions harmoniques Analytic functions Plurisubharmonic functions Plurisubharmonische Funktion (DE-588)4174927-3 gnd Analytische Funktion (DE-588)4142348-3 gnd |
| topic_facet | Fonctions analytiques Fonctions harmoniques Analytic functions Plurisubharmonic functions Plurisubharmonische Funktion Analytische Funktion Pluriharmonische Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001856589&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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