Potential theory on infinite networks:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1994
|
| Series: | Lecture notes in mathematics
1590 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 187 S. graph. Darst. |
| ISBN: | 354058448X |
Staff View
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| 100 | 1 | |a Soardi, Paolo M. |d 1946- |e Verfasser |0 (DE-588)114332746 |4 aut | |
| 245 | 1 | 0 | |a Potential theory on infinite networks |c Paolo M. Soardi |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1994 | |
| 300 | |a VIII, 187 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1590 | |
| 650 | 4 | |a Analyse de réseau (Planification) | |
| 650 | 7 | |a Netwerkanalyse |2 gtt | |
| 650 | 7 | |a Potentiaaltheorie |2 gtt | |
| 650 | 4 | |a Potentiel, Théorie du | |
| 650 | 4 | |a Network analysis (Planning) | |
| 650 | 4 | |a Potential theory (Mathematics) | |
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Record in the Search Index
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CONTENTS
Introduction vii
Chapter I. Kirchhoff's laws 1
0. Examples of infinite electrical networks 1
1. Graphs and networks 3
2. Chains and cochains 8
3. Kirchhoff's equations 12
4. The associated Markov chain 14
5. Harmonic functions 18
Chapter II. Finite networks 22
1. Existence and uniqueness of currents 22
2. The effective resistance 25
3. Three basic principles 28
Chapter III. Currents and potentials with finite energy 32
1. Finite energy and Dirichlet sums 32
2. Existence of currents with finite energy 36
3. The minimal current 39
4. Transient networks 43
5. Recurrent networks 46
6. Dirichlet's and Rayleigh's principles 51
7. Decomposition and approximation of functions in D 58
8. Extremal length 63
9. Limits of Dirichlet functions along paths 67
Chapter IV. Uniqueness and related topics 72
1. Spaces of cycles 72
2. Bounded automorphisms 74
3. Cartesian products 77
4. Nonuniqueness and ends 79
5. The strong isoperimetric inequality 81
6. Graphs embedded in the hyperbolic disk 89
7. Nonuniqueness and hyperbolic graphs 93
8. Moderate growth and Foster's averaging formula 96
Chapter V. Some examples and computations 100
1. Transience of infinite grids 100
2. Potentials in Z" 104
3. Ungrounded cascades 109
4. Grounded cascades. Generalized networks 113
VI
5. The strong isoperimetric inequality for trees 119
6. Capacity of the boundary of a tree 121
7. Edge graphs of tilings of the plane 125
Chapter VI. Royden's compactification 131
1. The algebra BD 131
2. Properties of Royden's compactification 134
3. Boundary points 139
4. The harmonic measure 146
5. Spaces HD of finite dimension 151
6. Compactification of subnetworks 154
Chapter VII. Rough isometries 160
1. Rough isometries in metric spaces 160
2. Some lemmas 161
3. Recurrence, class Ohd and rough isometries 166
4. Combinatorial boundaries 170
Appendix. Nonlinear networks 173
1. Nonlinear networks and modular sequence spaces 173
2. p networks 176
Bibliography 179
Index 184 |
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-20T07:38:04Z |
| institution | BVB |
| isbn | 354058448X |
| language | English |
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| physical | VIII, 187 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Soardi, Paolo M. 1946- Verfasser (DE-588)114332746 aut Potential theory on infinite networks Paolo M. Soardi Berlin [u.a.] Springer 1994 VIII, 187 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1590 Analyse de réseau (Planification) Netwerkanalyse gtt Potentiaaltheorie gtt Potentiel, Théorie du Network analysis (Planning) Potential theory (Mathematics) Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Netzwerktheorie (DE-588)4171531-7 gnd rswk-swf Netzwerk (DE-588)4171529-9 gnd rswk-swf Netzwerk (DE-588)4171529-9 s Potenzialtheorie (DE-588)4046939-6 s DE-604 Netzwerktheorie (DE-588)4171531-7 s Lecture notes in mathematics 1590 (DE-604)BV000676446 1590 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006477417&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Soardi, Paolo M. 1946- Potential theory on infinite networks Lecture notes in mathematics Analyse de réseau (Planification) Netwerkanalyse gtt Potentiaaltheorie gtt Potentiel, Théorie du Network analysis (Planning) Potential theory (Mathematics) Potenzialtheorie (DE-588)4046939-6 gnd Netzwerktheorie (DE-588)4171531-7 gnd Netzwerk (DE-588)4171529-9 gnd |
| subject_GND | (DE-588)4046939-6 (DE-588)4171531-7 (DE-588)4171529-9 |
| title | Potential theory on infinite networks |
| title_auth | Potential theory on infinite networks |
| title_exact_search | Potential theory on infinite networks |
| title_full | Potential theory on infinite networks Paolo M. Soardi |
| title_fullStr | Potential theory on infinite networks Paolo M. Soardi |
| title_full_unstemmed | Potential theory on infinite networks Paolo M. Soardi |
| title_short | Potential theory on infinite networks |
| title_sort | potential theory on infinite networks |
| topic | Analyse de réseau (Planification) Netwerkanalyse gtt Potentiaaltheorie gtt Potentiel, Théorie du Network analysis (Planning) Potential theory (Mathematics) Potenzialtheorie (DE-588)4046939-6 gnd Netzwerktheorie (DE-588)4171531-7 gnd Netzwerk (DE-588)4171529-9 gnd |
| topic_facet | Analyse de réseau (Planification) Netwerkanalyse Potentiaaltheorie Potentiel, Théorie du Network analysis (Planning) Potential theory (Mathematics) Potenzialtheorie Netzwerktheorie Netzwerk |
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