Differential equations on fractals: a tutorial
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton [u.a.]
Princeton Univ. Press
2006
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 169 S. graph. Darst. |
| ISBN: | 069112731X 9780691127316 0691125422 9780691125428 |
Staff View
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Record in the Search Index
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| adam_text | DIFFERENTIAL EQUATIONS ON FRACTALS A TUTORIAL ROBERT S. STRICHARTZ
PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD CONTENTS INTRODUCTION
VII 1 1 5 10 18 ; 23 27 29 31 31 34 37 41 44 46 55 62 CHAPTER 3.
SPECTRUM OF THE LAPLACIAN * 63 3.1 FOURIER SERIES REVISITED 63 3.2
SPECTRAL DECIMATION 68 3.3 EIGENVALUES AND MULTIPLICITIES 73 3.4
LOCALIZED EIGENFUNCTIONS 79 3.5 SPECTRAL ASYMPTOTICS 83 3.6 INTEGRALS
INVOLVING EIGENFUNCTIONS 86 3.7 NOTES AND REFERENCES 89 CHAPTER 4.
POSTCRITICALLY FINITE FRACTALS 91 4.1 DEFINITIONS , 91 4.2 ENERGY
RESTRICTION AND RENORMALIZATION 96 4.3 EXAMPLES 101 4.4 LAPLACIANS 109
4.5 GEOGRAPHY IS DESTINY 114 4.6 NON-SELF-SIMILAR FRACTALS 116 4.7 NOTES
AND REFERENCES 119 CHAPTER 1.1 1.2 1.3 1.4 1.5 1.6 1.7 CHAPTER 2.1 2.2
2.3 2.4 2.5 2.6 2.7 2.8 1. MEASURE, ENERGY, AND METRIC GRAPH
APPROXIMATIONS SELF-SIMILAR MEASURES GRAPH ENERGIES ENERGY ELECTRIC
NETWORK INTERPRETATION EFFECTIVE RESISTANCE METRIC NOTES AND REFERENCES
2. LAPLACIAN WEAK FORMULATION POINTWISE FORMULA NORMAL DERIVATIVES
GAUSS-GREEN FORMULA GLUING GREEN S FUNCTION LOCAL BEHAVIOR OF FUNCTIONS
NOTES AND REFERENCES VI CONTENTS CHAPTER 5. FURTHER TOPICS 121 5.1
POLYNOMIALS, SPLINES, AND POWER SERIES 121 5.2 LOCAL SYMMETRIES 125 5.3
ENERGY MEASURES 127 5.4 FRACTAL BLOW-UPS AND FRACTAFOLDS 131 5.5
SINGULARITIES 136 5.6 PRODUCTS OF FRACTALS 140 5.7 SOLVABILITY OF
DIFFERENTIAL EQUATIONS 146 5.8 HEAT KERNEL ESTIMATES 149 5.9 CONVERGENCE
OF FOURIER SERIES 152 5.10 NOTES AND REFERENCES 156 REFERENCES 159 INDEX
167
|
| adam_txt |
DIFFERENTIAL EQUATIONS ON FRACTALS A TUTORIAL ROBERT S. STRICHARTZ
PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD CONTENTS INTRODUCTION
VII 1 1 5 10 18 ; 23 27 29 31 31 34 37 41 44 46 55 62 CHAPTER 3.
SPECTRUM OF THE LAPLACIAN * 63 3.1 FOURIER SERIES REVISITED 63 3.2
SPECTRAL DECIMATION 68 3.3 EIGENVALUES AND MULTIPLICITIES 73 3.4
LOCALIZED EIGENFUNCTIONS 79 3.5 SPECTRAL ASYMPTOTICS 83 3.6 INTEGRALS
INVOLVING EIGENFUNCTIONS 86 3.7 NOTES AND REFERENCES 89 CHAPTER 4.
POSTCRITICALLY FINITE FRACTALS 91 4.1 DEFINITIONS , 91 4.2 ENERGY
RESTRICTION AND RENORMALIZATION 96 4.3 EXAMPLES 101 4.4 LAPLACIANS 109
4.5 GEOGRAPHY IS DESTINY 114 4.6 NON-SELF-SIMILAR FRACTALS 116 4.7 NOTES
AND REFERENCES 119 CHAPTER 1.1 1.2 1.3 1.4 1.5 1.6 1.7 CHAPTER 2.1 2.2
2.3 2.4 2.5 2.6 2.7 2.8 1. MEASURE, ENERGY, AND METRIC GRAPH
APPROXIMATIONS SELF-SIMILAR MEASURES GRAPH ENERGIES ENERGY ELECTRIC
NETWORK INTERPRETATION EFFECTIVE RESISTANCE METRIC NOTES AND REFERENCES
2. LAPLACIAN WEAK FORMULATION POINTWISE FORMULA NORMAL DERIVATIVES
GAUSS-GREEN FORMULA GLUING GREEN'S FUNCTION LOCAL BEHAVIOR OF FUNCTIONS
NOTES AND REFERENCES VI CONTENTS CHAPTER 5. FURTHER TOPICS 121 5.1
POLYNOMIALS, SPLINES, AND POWER SERIES 121 5.2 LOCAL SYMMETRIES 125 5.3
ENERGY MEASURES 127 5.4 FRACTAL BLOW-UPS AND FRACTAFOLDS 131 5.5
SINGULARITIES 136 5.6 PRODUCTS OF FRACTALS 140 5.7 SOLVABILITY OF
DIFFERENTIAL EQUATIONS 146 5.8 HEAT KERNEL ESTIMATES 149 5.9 CONVERGENCE
OF FOURIER SERIES 152 5.10 NOTES AND REFERENCES 156 REFERENCES 159 INDEX
167 |
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| isbn | 069112731X 9780691127316 0691125422 9780691125428 |
| language | English |
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| spelling | Strichartz, Robert S. Verfasser aut Differential equations on fractals a tutorial Robert S. Strichartz Princeton [u.a.] Princeton Univ. Press 2006 XIV, 169 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Fractales Équations différentielles Fractals Differential equations Fraktal (DE-588)4123220-3 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Fraktal (DE-588)4123220-3 s Differentialgleichung (DE-588)4012249-9 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014995003&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Strichartz, Robert S. Differential equations on fractals a tutorial Fractales Équations différentielles Fractals Differential equations Fraktal (DE-588)4123220-3 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4123220-3 (DE-588)4012249-9 |
| title | Differential equations on fractals a tutorial |
| title_auth | Differential equations on fractals a tutorial |
| title_exact_search | Differential equations on fractals a tutorial |
| title_exact_search_txtP | Differential equations on fractals a tutorial |
| title_full | Differential equations on fractals a tutorial Robert S. Strichartz |
| title_fullStr | Differential equations on fractals a tutorial Robert S. Strichartz |
| title_full_unstemmed | Differential equations on fractals a tutorial Robert S. Strichartz |
| title_short | Differential equations on fractals |
| title_sort | differential equations on fractals a tutorial |
| title_sub | a tutorial |
| topic | Fractales Équations différentielles Fractals Differential equations Fraktal (DE-588)4123220-3 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Fractales Équations différentielles Fractals Differential equations Fraktal Differentialgleichung |
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