Positive Harmonic Functions and Diffusion (Cambridge Studies in Advanced Mathematics, Series Number 45)

Pinsky, Ross G.

ISBN 10: 0521470145 / ISBN 13: 9780521470148

Editore: Cambridge University Press, 1995

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Titolo: Positive Harmonic Functions and Diffusion (...

Casa editrice: Cambridge University Press

Data di pubblicazione: 1995

Legatura: Rilegato

Condizione: Good

Descrizione articolo

Riassunto:

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.

Recensione:

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