Book Search:  

 

 
Google full text of our books:

bookjacket

Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)
Christopher D. Sogge

Paperback | 2014 | $75.00 / £52.00 | ISBN: 9780691160788
Hardcover | 2014 | $165.00 / £115.00 | ISBN: 9780691160757
208 pp. | 7 x 10 | 1 line illus. | SHOPPING CART

eBook | ISBN: 9781400850549 |
Our eBook editions are available from these online vendors

| Table of Contents
Preface[PDF] pdf-icon | Chapter 1[PDF] pdf-icon

Google full text of this book:
 

Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. Christopher Sogge gives a proof of the sharp Weyl formula for the distribution of eigenvalues of Laplace-Beltrami operators, as well as an improved version of the Weyl formula, the Duistermaat-Guillemin theorem under natural assumptions on the geodesic flow. Sogge shows that there is quantum ergodicity of eigenfunctions if the geodesic flow is ergodic.

Sogge begins with a treatment of the Hadamard parametrix before proving the first main result, the sharp Weyl formula. He avoids the use of Tauberian estimates and instead relies on sup-norm estimates for eigenfunctions. The author also gives a rapid introduction to the stationary phase and the basics of the theory of pseudodifferential operators and microlocal analysis. These are used to prove the Duistermaat-Guillemin theorem. Turning to the related topic of quantum ergodicity, Sogge demonstrates that if the long-term geodesic flow is uniformly distributed, most eigenfunctions exhibit a similar behavior, in the sense that their mass becomes equidistributed as their frequencies go to infinity.

Christopher D. Sogge is the J. J. Sylvester Professor of Mathematics at Johns Hopkins University. He is the author of Fourier Integrals in Classical Analysis and Lectures on Nonlinear Wave Equations.

Table of Contents

Series:

Subject Area:

VISIT OUR MATH WEBSITE

Shopping Cart:

  • For ebooks:

Our eBook editions are available
from these online vendors:

  • Amazon Kindle Store
  • Apple iBooks
  • Barnes & Noble Nook Store
  • Google Play eBook Store
  • Kno eBook Store
  • Kobo eBook Store
  • Many of our ebooks are available through
    library electronic resources including these platforms:

  • Books at JSTOR
  • Ebrary
  • Ebook Library
  • EBSCO Ebooks
  • MyiLibrary
  • Dawsonera (UK)

  • Shopping Cart:

    • For hardcover/paperback orders:

      For hardcover/paperback orders in the United States, Canada, Latin America, Asia, and Australia

      Paperback: $75.00 ISBN: 9780691160788

      Hardcover: $165.00 ISBN: 9780691160757

      For hardcover/paperback orders in Europe, Africa, the Middle East, and India

      Paperback: £52.00 ISBN: 9780691160788

      Add to shopping cart

      Hardcover: £115.00 ISBN: 9780691160757

      Add to shopping cart

      Prices subject to change without notice

      File created: 9/19/2014

    Questions and comments to: webmaster@press.princeton.edu
    Princeton University Press

    New Book E-mails
    New In Print
    PUP Blog
    Videos/Audios
    Princeton APPS
    Sample Chapters
    Subjects
    Series
    Catalogs
    Princeton Legacy Library
    Textbooks
    Media/Reviewers
    Class Use
    Rights/Permissions
    Ordering
    Recent Awards
    Princeton Shorts
    Freshman Reading
    PUP Europe
    About Us
    Contact Us
    Links
    F.A.Q.
    MATH SITE
    PUP Home


    Bookmark and Share
    Send me emails
    about new books in:
    Mathematics
    More Choices
    Email:
    Country:
    Name: