| Description |
1 online resource (130 pages) |
| Series |
Memoirs of the American Mathematical Society ; no. 1250 |
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Memoirs of the American Mathematical Society ; no. 1250.
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| Contents |
Cover; Title page; Chapter 1. Introduction; Chapter 2. Generalized Sierpinski carpets; Chapter 3. Standing assumptions and notations; Chapter 4. Gauge function; Chapter 5. The Brownian motion and the Green function; Chapter 6. Time change of the Brownian motion; Chapter 7. Scaling of the Green function; Chapter 8. Resolvents; Chapter 9. Poincaré inequality; Chapter 10. Heat kernel, existence and continuity; Chapter 11. Measures having weak exponential decay; Chapter 12. Protodistance and diagonal lower estimateof heat kernel; Chapter 13. Proof of Theorem 1.1 |
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Chapter 14. Random measures having weak exponential decayChapter 15. Volume doubling measure and sub-Gaussian heat kernel estimate; Chapter 16. Examples; Chapter 17. Construction of metrics from gauge function; Chapter 18. Metrics and quasimetrics; Chapter 19. Protodistance and the volume doubling property; Chapter 20. Upper estimate of _{ }(,); Chapter 21. Lower estimate of _{ }(,); Chapter 22. Non existence of super-Gaussian heat kernel behavior; Bibliography; List of Notations; Index; Back Cover |
| Summary |
In this paper, time changes of the Brownian motions on generalized Sierpinski carpets including n-dimensional cube [0, 1]̂n are studied. Intuitively time change corresponds to alteration to density of the medium where the heat flows. In case of the Brownian motion on [0, 1]̂n, density of the medium is homogeneous and represented by the Lebesgue measure. The author's study includes densities which are singular to the homogeneous one. He establishes a rich class of measures called measures having weak exponential decay. This class contains measures which are singular to the homogeneous one such |
| Notes |
Print version record |
| Subject |
Brownian motion processes.
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Mathematical analysis.
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Heat -- Transmission.
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heat transmission.
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Análisis matemático
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Movimientos brownianos
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Calor-Transmisión
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Brownian motion processes
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Heat -- Transmission
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Mathematical analysis
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| Form |
Electronic book
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| ISBN |
1470452553 |
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9781470452551 |
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