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Positive Harmonic Functions: 45 (Cambridge Studies in Advanced Mathematics, Series Number 45) - Softcover
Inhaltsangabe
Professor Pinsky gives a self-contained account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach. A useful reference for the specialist, and an excellent guide for the graduate student.
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Críticas
Review of the hardback: 'This book is reasonably self contained, accessible even to a graduate student but maintaining a high level of mathematical rigor.' European Mathematical Society Newsletter
Reseña del editor
In this book, Professor Pinsky gives a self-contained account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach. The book begins with a treatment of the construction and basic properties of diffusion processes. This theory then serves as a vehicle for studying positive harmonic funtions. Starting with a rigorous treatment of the spectral theory of elliptic operators with nice coefficients on smooth, bounded domains, the author then develops the theory of the generalized principal eigenvalue, and the related criticality theory for elliptic operators on arbitrary domains. Martin boundary theory is considered, and the Martin boundary is explicitly calculated for several classes of operators. The book provides an array of criteria for determining whether a diffusion process is transient or recurrent. Also introduced are the theory of bounded harmonic functions, and Brownian motion on manifolds of negative curvature. Many results that form the folklore of the subject are here given a rigorous exposition, making this book a useful reference for the specialist, and an excellent guide for the graduate student.
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- VerlagCambridge University Press
- Erscheinungsdatum2008
- ISBN 10 0521059836
- ISBN 13 9780521059831
- EinbandTapa blanda
- SpracheEnglisch
- Anzahl der Seiten492
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Positive Harmonic Functions and Diffusion (Cambridge Studies in Advanced Mathematics, Series Number 45)
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Positive Harmonic Functions and Diffusion
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - A self-contained account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach. Artikel-Nr. 9780521059831
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