Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194) - Annals of Mathematics Studies 356 (Paperback)
  • Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194) - Annals of Mathematics Studies 356 (Paperback)
zoom

Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194) - Annals of Mathematics Studies 356 (Paperback)

(author), (author)
£58.00
Paperback 272 Pages / Published: 14/06/2016
  • We can order this

Usually dispatched within 1 week

  • This item has been added to your basket
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.

Publisher: Princeton University Press
ISBN: 9780691170558
Number of pages: 272
Weight: 397 g
Dimensions: 235 x 152 x 15 mm

You may also be interested in...

Platonic and Archimedean Solids
Added to basket
A Geometry of Music
Added to basket
Differential Geometry
Added to basket
Drawing Geometry
Added to basket
£12.99
Paperback
Elliptic Tales
Added to basket
£13.99
Paperback
Fractals: A Very Short Introduction
Added to basket
Euclid's Elements
Added to basket
£31.99
Hardback
Measurement
Added to basket
£16.95
Paperback
Euclid's Elements
Added to basket
£21.99
Paperback
Introducing Fractals
Added to basket
Visual Complex Analysis
Added to basket
Mathematical Origami
Added to basket
An Introduction to Manifolds
Added to basket
Maths for Science
Added to basket
£37.99
Paperback
Islamic Design
Added to basket
£5.99
Paperback

Please sign in to write a review

Your review has been submitted successfully.