Google full text of our books:

     
bookjacket

Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)
Isroil A. Ikromov & Detlef Müller

Paperback | 2016 | $75.00 | £62.95 | ISBN: 9780691170558
Hardcover | 2016 | $165.00 | £137.95 | ISBN: 9780691170541
272 pp. | 6 x 9 1/4 | 7 line illus.
Add to Shopping Cart

eBook | ISBN: 9781400881246 |
Our eBook editions are available from these online vendors

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

Google full text of this book:
 

This is the first book to present a complete characterization of Stein-Tomas type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all real-analytic hypersurfaces. The range of Lebesgue spaces for which these estimates are valid is described in terms of Newton polyhedra associated to the given surface.

Isroil Ikromov and Detlef Müller begin with Elias M. Stein's concept of Fourier restriction and some relations between the decay of the Fourier transform of the surface measure and Stein-Tomas type restriction estimates. Varchenko's ideas relating Fourier decay to associated Newton polyhedra are briefly explained, particularly the concept of adapted coordinates and the notion of height. It turns out that these classical tools essentially suffice already to treat the case where there exist linear adapted coordinates, and thus Ikromov and Müller concentrate on the remaining case. Here the notion of r-height is introduced, which proves to be the right new concept. They then describe decomposition techniques and related stopping time algorithms that allow to partition the given surface into various pieces, which can eventually be handled by means of oscillatory integral estimates. Different interpolation techniques are presented and used, from complex to more recent real methods by Bak and Seeger.

Fourier restriction plays an important role in several fields, in particular in real and harmonic analysis, number theory, and PDEs. This book will interest graduate students and researchers working in such fields.

Isroil A. Ikromov is professor of mathematics at Samarkand State University in Uzbekistan. Detlef Müller is professor of mathematics at the University of Kiel in Germany.

Table of Contents

Link:

Series:

Subject Area:

VISIT OUR MATH WEBSITE

Shopping Cart options:

  • For ebooks:

Our eBook editions are available
from these online vendors:

  • Amazon Kindle Store
  • Apple iBooks
  • Barnes & Noble Nook Store
  • Google Play 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)

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

     Paperback : $75.00 ISBN: 9780691170558

    Add to shopping cart

     Hardcover : $165.00 ISBN: 9780691170541

    Add to shopping cart
    View contents of your shopping cart

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

     Hardcover  £137.95 ISBN: 9780691170541

    Add to shopping cart

     Paperback  £62.95 ISBN: 9780691170558

    Add to shopping cart
    View contents of your shopping cart

    Prices subject to change without notice

    File created: 9/7/2017

    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
    Exam/Desk Copy
    Textbooks
    Media/Reviewers
    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