Description: Further DetailsTitle: Fourier Restriction for Hypersurfaces in Three Dimensions and Newton PolyhedraCondition: NewEAN: 9780691170541ISBN: 9780691170541Publisher: Princeton University PressFormat: HardbackRelease Date: 05/24/2016Item Height: 235mmItem Length: 152mmItem Weight: 510gAuthor: Isroil A. Ikromov, Detlef MüllerLanguage: EnglishISBN-10: 0691170541Description: 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 Muller 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 Muller 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.Country/Region of Manufacture: USGenre: Science Nature & MathBook Series: Annals of Mathematics StudiesRelease Year: 2016 Missing Information?Please contact us if any details are missing and where possible we will add the information to our listing.
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Book Title: Fourier Restriction for Hypersurfaces in Three Dimensions and New
Title: Fourier Restriction for Hypersurfaces in Three Dimensions and New
EAN: 9780691170541
ISBN: 9780691170541
Release Date: 05/24/2016
Release Year: 2016
ISBN-10: 0691170541
Country/Region of Manufacture: US
Genre: Science Nature & Math
Number of Pages: 272 Pages
Language: English
Publication Name: Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra
Publisher: Oxford University Press, Incorporated
Subject: Geometry / General, Algebra / General, Topology, Geometry / Algebraic, Mathematical Analysis
Item Height: 0.8 in
Publication Year: 2016
Type: Textbook
Item Weight: 18 Oz
Author: Isroil A. Ikromov, Detlef Müller
Subject Area: Mathematics
Item Length: 9.5 in
Series: Annals of Mathematics Studies
Item Width: 6.1 in
Format: Hardcover
