Positive Harmonic Functions and Diffusion

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Hardcover | 13 March 1995

At a Glance

Hardcover
492 Pages

Dimensions(cm)
22.86 x 15.24 x 3.18

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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 functions. 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.

Industry Reviews

From the hardback review: 'This book is reasonably self contained, accessible even to a graduate student but maintaining a high level of mathematical rigor.' European Mathematical Society Newsletter

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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
Table of Contents provided by Publisher. All Rights Reserved.

Positive Harmonic Functions and Diffusion

At a Glance

Hardcover

Industry Reviews

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How to return your order

Defective items

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