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Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra / / Isroil A. Ikromov and Detlef Müller



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Autore: Ikromov Isroil A. <1961-> Visualizza persona
Titolo: Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra / / Isroil A. Ikromov and Detlef Müller Visualizza cluster
Pubblicazione: Princeton : , : Princeton University Press, , [2016]
Descrizione fisica: 1 online resource (269 p.)
Disciplina: 516.3/52
Soggetto topico: Hypersurfaces
Polyhedra
Surfaces, Algebraic
Fourier analysis
Soggetto non controllato: Airy cone
Airy-type analysis
Airy-type decompositions
Fourier decay
Fourier integral
Fourier restriction estimate
Fourier restriction problem
Fourier restriction theorem
Fourier restriction
Fourier transform
Greenleaf's restriction
Lebesgue spaces
LittlewoodАaley decomposition
LittlewoodАaley theory
Newton polyhedra
Newton polyhedral
Newton polyhedron
SteinДomas-type Fourier restriction
auxiliary results
complex interpolation
dyadic decomposition
dyadic decompositions
dyadic domain decompositions
endpoint estimates
endpoint result
improved estimates
interpolation arguments
interpolation theorem
invariant description
linear coordinates
linearly adapted coordinates
normalized measures
normalized rescale measures
one-dimensional oscillatory integrals
open cases
operator norms
phase functions
preparatory results
principal root jet
propositions
r-height
real interpolation
real-analytic hypersurface
refined Airy-type analysis
restriction estimates
restriction
smooth hypersurface
smooth hypersurfaces
spectral localization
stopping-time algorithm
sublevel type
thin sets
three dimensions
transition domains
uniform bounds
van der Corput-type estimates
Classificazione: SI 830
Persona (resp. second.): MüllerDetlef <1954->
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references and index.
Nota di contenuto: Frontmatter -- Contents -- Chapter 1. Introduction -- Chapter 2. Auxiliary Results -- Chapter 3. Reduction to Restriction Estimates near the Principal Root Jet -- Chapter 4. Restriction for Surfaces with Linear Height below 2 -- Chapter 5. Improved Estimates by Means of Airy-Type Analysis -- Chapter 6. The Case When hlin(Φ) ≥ 2: Preparatory Results -- Chapter 7. How to Go beyond the Case hlin(Φ) ≥ 5 -- Chapter 8. The Remaining Cases Where m = 2 and B = 3 or B = 4 -- Chapter 9. Proofs of Propositions 1.7 and 1.17 -- Bibliography -- Index
Sommario/riassunto: 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.
Titolo autorizzato: Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra  Visualizza cluster
ISBN: 1-4008-8124-2
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910798386803321
Lo trovi qui: Univ. Federico II
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Serie: Annals of mathematics studies ; ; number 194.