Positive Harmonic Functions and Diffusion

Name: Positive Harmonic Functions and Diffusion
Price: 162.47 USD
Availability: InStock
ISBN: 9780521470148

ISBN-10: 0521470145

ISBN-13: 9780521470148

Edition: 1995

Authors: Ross G. Pinsky, B. Bollobas, W. Fulton, A. Katok, F. Kirwan

List price: $244.99

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Description:

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…

Book details

List price: $244.99
Copyright year: 1995
Publisher: Cambridge University Press
Publication date: 1/12/1995
Binding: Hardcover
Pages: 492
Size: 6.75" wide x 9.75" long x 1.25" tall
Weight: 1.738
Language: English




Existence and uniqueness for diffusion processes



The basic properties of diffusion processes



The spectral theory of elliptic operators on smooth bounded domains



Generalized spectral theory for operators on arbitrary domains



Applications to the one-dimensional case and the radially symmetric multi-dimensional case



Criteria for transience or recurrence and explosion or non-explosion of diffusion processes



Positive harmonic functions and the Martin boundary: general theory



Positive harmonic functions and the Martin boundary: applications to certain classes of operators



Bounded harmonic functions and applications to Brownian motion and the Laplacian on a manifold of non-positive curvature