Analysis on fractals:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2001
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge tracts in mathematics
143 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 226 S. graph. Darst, |
| ISBN: | 0521793211 |
Internformat
MARC
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| 100 | 1 | |a Kigami, Jun |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Analysis on fractals |c Jun Kigami |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 2001 | |
| 300 | |a VIII, 226 S. |b graph. Darst, | ||
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Datensatz im Suchindex
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| adam_text | Contents
Introduction 1
1 Geometry of Self Similar Sets 8
1.1 Construction of self similar sets 8
1.2 Shift space and self similar sets 12
1.3 Self similar structure 17
1.4 Self similar measure 25
1.5 Dimension of self similar sets 28
1.6 Connectivity of self similar sets 33
Notes and references 38
Exercises 39
2 Analysis on Limits of Networks 41
2.1 Dirichlet forms and Laplacians on a finite set 41
2.2 Sequence of discrete Laplacians 51
2.3 Resistance form and resistance metric 55
2.4 Dirichlet forms and Laplacians on limits of networks 63
Notes and references 66
Exercises 66
3 Construction of Laplacians on P. C. F. Self Similar
Structures 68
3.1 Harmonic structures 69
3.2 Harmonic functions 73
3.3 Topology given by effective resistance 83
3.4 Dirichlet forms on p. c. f. self similar sets 88
3.5 Green s function 94
3.6 Green s operator 102
3.7 Laplacians 107
3.8 Nested fractals 115
Notes and references 127
vii
viii Contents
Exercises 128
4 Eigenvalues and Eigenfunctions of Laplacians 131
4.1 Eigenvalues and eigenfunctions 132
4.2 Relation between dimensions 137
4.3 Localized eigenfunctions 141
4.4 Existence of localized eigenfunctions 146
4.5 Estimate of eigenfunctions 152
Notes and references 155
5 Heat Kernels 157
5.1 Construction of heat kernels 158
5.2 Parabolic maximum principle 164
5.3 Asymptotic behavior of the heat kernels 171
Notes and references 178
Appendix 180
A Additional Facts 180
A.I Second eigenvalue of Aj 180
A.2 General boundary conditions 185
A.3 Probabilistic approach 193
B Mathematical Background 196
B.I Self adjoint operators and quadratic forms 196
B.2 Semigroups 199
B.3 Dirichlet forms and the Nash inequality 202
B.4 The renewal theorem 207
Bibliography 212
Index of Notation 221
Index 222
|
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| id | DE-604.BV013752199 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:51:22Z |
| institution | BVB |
| isbn | 0521793211 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009400927 |
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| physical | VIII, 226 S. graph. Darst, |
| publishDate | 2001 |
| publishDateSearch | 2001 |
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| publisher | Cambridge Univ. Press |
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| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Kigami, Jun Verfasser aut Analysis on fractals Jun Kigami 1. publ. Cambridge Cambridge Univ. Press 2001 VIII, 226 S. graph. Darst, txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 143 Fraktal - Dynamisches System Analysis (DE-588)4001865-9 gnd rswk-swf Fraktal (DE-588)4123220-3 gnd rswk-swf Fraktal (DE-588)4123220-3 s Analysis (DE-588)4001865-9 s DE-604 Cambridge tracts in mathematics 143 (DE-604)BV000000001 143 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009400927&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kigami, Jun Analysis on fractals Cambridge tracts in mathematics Fraktal - Dynamisches System Analysis (DE-588)4001865-9 gnd Fraktal (DE-588)4123220-3 gnd |
| subject_GND | (DE-588)4001865-9 (DE-588)4123220-3 |
| title | Analysis on fractals |
| title_auth | Analysis on fractals |
| title_exact_search | Analysis on fractals |
| title_full | Analysis on fractals Jun Kigami |
| title_fullStr | Analysis on fractals Jun Kigami |
| title_full_unstemmed | Analysis on fractals Jun Kigami |
| title_short | Analysis on fractals |
| title_sort | analysis on fractals |
| topic | Fraktal - Dynamisches System Analysis (DE-588)4001865-9 gnd Fraktal (DE-588)4123220-3 gnd |
| topic_facet | Fraktal - Dynamisches System Analysis Fraktal |
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