| 000 | 07884cam a2200949 i 4500 | ||
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| 001 | ocn949276252 | ||
| 003 | OCoLC | ||
| 005 | 20220908100111.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 160510s2016 nju ob 001 0 eng d | ||
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| 049 | _aMAIN | ||
| 100 | 1 |
_aIkromov, Isroil A., _d1961- _eauthor. _964759 |
|
| 245 | 1 | 0 |
_aFourier restriction for hypersurfaces in three dimensions and Newton polyhedra / _cIsroil A. Ikromov and Detlef M�uller. |
| 264 | 1 |
_aPrinceton : _bPrinceton University Press, _c[2016] |
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| 300 | _a1 online resource | ||
| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 490 | 1 |
_aAnnals of mathematics studies ; _vnumber 194 |
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| 504 | _aIncludes bibliographical references and index. | ||
| 588 | 0 | _aPrint version record. | |
| 505 | 0 | 0 |
_6880-01 _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 h -- _tChapter 7. How to Go beyond the Case h -- _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. |
| 520 | _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 M�uller 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 M�uller 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. | ||
| 590 |
_aIEEE _bIEEE Xplore Princeton University Press eBooks Library |
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| 650 | 0 |
_aHypersurfaces. _964760 |
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| 650 | 0 |
_aPolyhedra. _964761 |
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| 650 | 0 |
_aSurfaces, Algebraic. _964762 |
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| 650 | 0 |
_aFourier analysis. _96642 |
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| 650 | 2 |
_aFourier Analysis _96642 |
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| 650 | 6 |
_aHypersurfaces. _964760 |
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| 650 | 6 |
_aPoly�edres. _964763 |
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| 650 | 6 |
_aSurfaces alg�ebriques. _964764 |
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| 650 | 6 |
_aAnalyse de Fourier. _964765 |
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| 650 | 7 |
_apolyhedra. _2aat _964766 |
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| 650 | 7 |
_aMATHEMATICS _xGeometry _xGeneral. _2bisacsh _97661 |
|
| 650 | 7 |
_aFourier analysis. _2fast _0(OCoLC)fst00933401 _96642 |
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| 650 | 7 |
_aHypersurfaces. _2fast _0(OCoLC)fst00965830 _964760 |
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| 650 | 7 |
_aPolyhedra. _2fast _0(OCoLC)fst01070511 _964761 |
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| 650 | 7 |
_aSurfaces, Algebraic. _2fast _0(OCoLC)fst01139295 _964762 |
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| 655 | 0 |
_aElectronic books. _93294 |
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| 655 | 4 |
_aElectronic books. _93294 |
|
| 700 | 1 |
_aM�uller, Detlef, _d1954- _eauthor. _964767 |
|
| 776 | 0 | 8 |
_iPrint version: _aIkromov, Isroil A., 1961- _tFourier restriction for hypersurfaces in three dimensions and Newton polyhedra. _dPrinceton : Princeton University Press, [2016] _z9780691170541 _w(DLC) 2015041649 _w(OCoLC)926820349 |
| 830 | 0 |
_aAnnals of mathematics studies ; _vno. 194. _964768 |
|
| 856 | 4 | 0 | _uhttps://ieeexplore.ieee.org/servlet/opac?bknumber=9452407 |
| 880 | 0 |
_6505-01/Grek _aCover -- Title -- Copyright -- Dedication -- Contents -- Chapter 1 Introduction -- 1.1 Newton Polyhedra Associated with ϕ, Adapted Coordinates, and Uniform Estimates for Oscillatory Integrals with Phase ϕ -- 1.2 Fourier Restriction in the Presence of a Linear Coordinate System That Is Adapted to ϕ -- 1.3 Fourier Restriction When No Linear Coordinate System Is Adapted to ϕ-the Analytic Case -- 1.4 Smooth Hypersurfaces of Finite Type, Condition (R), and the General Restriction Theorem -- 1.5 An Invariant Description of the Notion of r-Height. -- 1.6 Organization of the Monograph and Strategy of Proof -- Chapter 2 Auxiliary Results -- 2.1 Van der Corput-Type Estimates -- 2.2 Airy-Type Integrals -- 2.3 Integral Estimates of van der Corput Type -- 2.4 Fourier Restriction via Real Interpolation -- 2.5 Uniform Estimates for Families of Oscillatory Sums -- 2.6 Normal Forms of ϕ under Linear Coordinate Changes When hlin(ϕ) <2 -- Chapter 3 Reduction to Restriction Estimates near the Principal Root Jet -- Chapter 4 Restriction for Surfaces with Linear Height below 2 -- 4.1 Preliminary Reductions by Means of Littlewood-Paley Decompositions -- 4.2 Restriction Estimates for Normalized Rescaled Measures When 2^2j (Se(B3 ≲ 1 -- Chapter 5 Improved Estimates by Means of Airy-Type Analysis -- 5.1 Airy-Type Decompositions Required for Proposition 4.2(c) -- 5.2 The Endpoint in Proposition 4.2(c): Complex Interpolation -- 5.3 Proof of Proposition 4.2(a), (b): Complex Interpolation -- Chapter 6 The Case When hlin(ϕ) ≥ 2: Preparatory Results -- 6.1 The First Domain Decomposition -- 6.2 Restriction Estimates in the Transition Domains El When hlin(ϕ) ≥ 2 -- 6.3 Restriction Estimates in the Domains Dl, l <lpr, When hlin(ϕ)≥2 -- 6.4 Restriction Estimates in the Domain Dpr When hlin(ϕ)≥ 5. |
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