Dirichlet integrals on harmonic spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1980
|
| Series: | Lecture notes in mathematics
803 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 178 S. |
| ISBN: | 3540099956 0387099956 |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Introduction VII
Terminology and notation IX
Part I Theory on General Harmonic Spaces
§1. Harmonic spaces
1-1. Definition of harmonic spaces 1
1-2. Brelot s harmonic space 3
1-3. Bauer-Boboc-Constantinescu-Cornea s harmonic space 6
1-4. Examples 9
1-5. Properties of the base space of a harmonic space 11
1-6. Properties of hyperharmonic functions 13
§2. Superharmonic functions and potentials
2-1. Superharmonic functions 16
2-2. Potentials 18
2-3. Reduced functions 20
2-4. P-sets 22
2-5. The space 7 V) 28
§3. Gradient measures
3-1. Measure representations 33
3-2. Existence of measure representations on Brelot s harmonic spaces 35
3-3. Properties of measure representations 38
3-4. Definition of gradient measures 41
3-5. Basic properties of gradient measures 44
3-6. Composition of functions in X(U) with C2-functions 47
3-7. The case where X is a Euclidean domain 54
Part II Green s Formulae on Self-adjoint Harmonic Spaces
§4. Self-adjoint harmonic spaces and Green potentials
4-1. Dirichlet problems 56
4-2. Symmetric Green functions 61
4-3. Self-adj oint harmonic spaces 63
4-4. Fundamental properties of Green potentials 67
4-5. Canonical measure representation 69
4-6. PB-domains 71
4-7. Energy principle 76
VI
4-8. Green s formula for functions in Q (U) 80
§5. Energy-finite harmonic functions and Green s formula
5-1. Preliminary lemmas 86
5-2. Bounded energy-finite harmonic functions and preliminary Green s
formula 91
5-3. Green s formula on PB-domains 94
5-4. Green s formula for general open sets 98
Part III Spaces of Dirichlet-finite and Energy-finite Functions on Self-adjoint
Harmonic Spaces
§6. Spaces of Dirichlet-finite and energy-finite harmonic functions
6-1. Harnack s inequality 101
6-2. Lattice structures 103
6-3. Boundedness 108
6-4. Completeness 115
6-5. The space of energy-finite functions and decomposition theorems 119
6-6. Density of 3^£(U) in 3^,(U) 129
§7. Functional completion
7-1. Completion of »(U) 134
7-2. Extension of Green s formula and its applications 139
7-3. Spaces ^CU), «JD(U),.8E)0(U) and^^CU) 143
7-4. Another extension of Green s formula 149
7-5. Royden decomposition 151
§8. Royden boundary
8-1. Royden algebra 154
8-2. Royden boundary 159
8-3. Normal derivatives and Neumann problems 163
APPENDIX : Networks 170
References 177
Index of terminologies 179
Index of symbols 180
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:42:58Z |
| institution | BVB |
| isbn | 3540099956 0387099956 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001486259 |
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| physical | X, 178 S. |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Maeda, Fumi-Yuki Verfasser aut Dirichlet integrals on harmonic spaces Fumi-Yuki Maeda Berlin [u.a.] Springer 1980 X, 178 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 803 Dirichlet, Intégrales de Espaces harmoniques Potentiel, Théorie du Harmonic spaces Integrals, Dirichlet Potential theory (Mathematics) Dirichletsches Integral (DE-588)4150140-8 gnd rswk-swf Harmonischer Raum (DE-588)4159130-6 gnd rswk-swf Dirichletsches Integral (DE-588)4150140-8 s Harmonischer Raum (DE-588)4159130-6 s DE-604 Lecture notes in mathematics 803 (DE-604)BV000676446 803 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001486259&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Maeda, Fumi-Yuki Dirichlet integrals on harmonic spaces Lecture notes in mathematics Dirichlet, Intégrales de Espaces harmoniques Potentiel, Théorie du Harmonic spaces Integrals, Dirichlet Potential theory (Mathematics) Dirichletsches Integral (DE-588)4150140-8 gnd Harmonischer Raum (DE-588)4159130-6 gnd |
| subject_GND | (DE-588)4150140-8 (DE-588)4159130-6 |
| title | Dirichlet integrals on harmonic spaces |
| title_auth | Dirichlet integrals on harmonic spaces |
| title_exact_search | Dirichlet integrals on harmonic spaces |
| title_full | Dirichlet integrals on harmonic spaces Fumi-Yuki Maeda |
| title_fullStr | Dirichlet integrals on harmonic spaces Fumi-Yuki Maeda |
| title_full_unstemmed | Dirichlet integrals on harmonic spaces Fumi-Yuki Maeda |
| title_short | Dirichlet integrals on harmonic spaces |
| title_sort | dirichlet integrals on harmonic spaces |
| topic | Dirichlet, Intégrales de Espaces harmoniques Potentiel, Théorie du Harmonic spaces Integrals, Dirichlet Potential theory (Mathematics) Dirichletsches Integral (DE-588)4150140-8 gnd Harmonischer Raum (DE-588)4159130-6 gnd |
| topic_facet | Dirichlet, Intégrales de Espaces harmoniques Potentiel, Théorie du Harmonic spaces Integrals, Dirichlet Potential theory (Mathematics) Dirichletsches Integral Harmonischer Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001486259&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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