Skip to content
Register Sign in Wishlist

Positive Harmonic Functions and Diffusion

£76.99

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: April 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521059831

£ 76.99
Paperback

Add to cart Add to wishlist

Other available formats:
Hardback, eBook


Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • 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.

    • Author is expert on subject
    • Possible supplementary text for graduate course
    Read more

    Reviews & endorsements

    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

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: April 2008
    • format: Paperback
    • isbn: 9780521059831
    • length: 492 pages
    • dimensions: 228 x 152 x 30 mm
    • weight: 0.773kg
    • availability: Available
  • Table of Contents

    1. Existence and uniqueness for diffusion processes
    2. The basic properties of diffusion processes
    3. The spectral theory of elliptic operators on smooth bounded domains
    4. Generalized spectral theory for operators on arbitrary domains
    5. Applications to the one-dimensional case and the radially symmetric multi-dimensional case
    6. Criteria for transience or recurrence and explosion or non-explosion of diffusion processes
    7. Positive harmonic functions and the Martin boundary: general theory
    8. Positive harmonic functions and the Martin boundary: applications to certain classes of operators
    9. Bounded harmonic functions and applications to Brownian motion and the Laplacian on a manifold of non-positive curvature.

  • Author

    Ross G. Pinsky

Related Books

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon
×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×