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100   $a20151030d2016      uy|            0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aFourier restriction for hypersurfaces in three dimensions and Newton polyhedra /$fIsroil A. Ikromov and Detlef Mu?ller
210  1$aPrinceton :$cPrinceton University Press,$d[2016]
215   $a1 online resource (269 p.)
225 1 $aAnnals of mathematics studies ;$vnumber 194
300   $aDescription based upon print version of record.
311   $a0-691-17055-X 
311   $a0-691-17054-1 
320   $aIncludes bibliographical references and index.
327   $tFrontmatter -- $tContents -- $tChapter 1. Introduction -- $tChapter 2. Auxiliary Results -- $tChapter 3. Reduction to Restriction Estimates near the Principal Root Jet -- $tChapter 4. Restriction for Surfaces with Linear Height below 2 -- $tChapter 5. Improved Estimates by Means of Airy-Type Analysis -- $tChapter 6. The Case When hlin(?) ? 2: Preparatory Results -- $tChapter 7. How to Go beyond the Case hlin(?) ? 5 -- $tChapter 8. The Remaining Cases Where m = 2 and B = 3 or B = 4 -- $tChapter 9. Proofs of Propositions 1.7 and 1.17 -- $tBibliography -- $tIndex
330   $aThis is the first book to present a complete characterization of Stein-Tomas type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all real-analytic hypersurfaces. The range of Lebesgue spaces for which these estimates are valid is described in terms of Newton polyhedra associated to the given surface.Isroil Ikromov and Detlef Müller begin with Elias M. Stein's concept of Fourier restriction and some relations between the decay of the Fourier transform of the surface measure and Stein-Tomas type restriction estimates. Varchenko's ideas relating Fourier decay to associated Newton polyhedra are briefly explained, particularly the concept of adapted coordinates and the notion of height. It turns out that these classical tools essentially suffice already to treat the case where there exist linear adapted coordinates, and thus Ikromov and Müller concentrate on the remaining case. Here the notion of r-height is introduced, which proves to be the right new concept. They then describe decomposition techniques and related stopping time algorithms that allow to partition the given surface into various pieces, which can eventually be handled by means of oscillatory integral estimates. Different interpolation techniques are presented and used, from complex to more recent real methods by Bak and Seeger.Fourier restriction plays an important role in several fields, in particular in real and harmonic analysis, number theory, and PDEs. This book will interest graduate students and researchers working in such fields.
410  0$aAnnals of mathematics studies ;$vnumber 194.
606   $aHypersurfaces
606   $aPolyhedra
606   $aSurfaces, Algebraic
606   $aFourier analysis
610   $aAiry cone.
610   $aAiry-type analysis.
610   $aAiry-type decompositions.
610   $aFourier decay.
610   $aFourier integral.
610   $aFourier restriction estimate.
610   $aFourier restriction problem.
610   $aFourier restriction theorem.
610   $aFourier restriction.
610   $aFourier transform.
610   $aGreenleaf's restriction.
610   $aLebesgue spaces.
610   $aLittlewood?aley decomposition.
610   $aLittlewood?aley theory.
610   $aNewton polyhedra.
610   $aNewton polyhedral.
610   $aNewton polyhedron.
610   $aStein?omas-type Fourier restriction.
610   $aauxiliary results.
610   $acomplex interpolation.
610   $adyadic decomposition.
610   $adyadic decompositions.
610   $adyadic domain decompositions.
610   $aendpoint estimates.
610   $aendpoint result.
610   $aimproved estimates.
610   $ainterpolation arguments.
610   $ainterpolation theorem.
610   $ainvariant description.
610   $alinear coordinates.
610   $alinearly adapted coordinates.
610   $anormalized measures.
610   $anormalized rescale measures.
610   $aone-dimensional oscillatory integrals.
610   $aopen cases.
610   $aoperator norms.
610   $aphase functions.
610   $apreparatory results.
610   $aprincipal root jet.
610   $apropositions.
610   $ar-height.
610   $areal interpolation.
610   $areal-analytic hypersurface.
610   $arefined Airy-type analysis.
610   $arestriction estimates.
610   $arestriction.
610   $asmooth hypersurface.
610   $asmooth hypersurfaces.
610   $aspectral localization.
610   $astopping-time algorithm.
610   $asublevel type.
610   $athin sets.
610   $athree dimensions.
610   $atransition domains.
610   $auniform bounds.
610   $avan der Corput-type estimates.
615  0$aHypersurfaces.
615  0$aPolyhedra.
615  0$aSurfaces, Algebraic.
615  0$aFourier analysis.
676   $a516.3/52
686   $aSI 830$2rvk
700   $aIkromov$b Isroil A.$f1961-$01566820
702   $aMu?ller$b Detlef$f1954-
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910798386803321
996   $aFourier restriction for hypersurfaces in three dimensions and Newton polyhedra$93837699
997   $aUNINA