Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra / (Record no. 81341)
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| Language of cataloging | eng |
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| 019 ## - | |
| -- | 1055344533 |
| -- | 1066600074 |
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| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781400881246 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 1400881242 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780691170541 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 0691170541 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780691170558 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 069117055X |
| 029 1# - OTHER SYSTEM CONTROL NUMBER (OCLC) | |
| OCLC library identifier | AU@ |
| System control number | 000060429874 |
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| OCLC library identifier | CHBIS |
| System control number | 010896085 |
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| System control number | BV043979302 |
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| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)949276252 |
| Canceled/invalid control number | (OCoLC)1055344533 |
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| 037 ## - SOURCE OF ACQUISITION | |
| Stock number | 22573/ctt194t8sv |
| Source of stock number/acquisition | JSTOR |
| 037 ## - SOURCE OF ACQUISITION | |
| Stock number | 9452407 |
| Source of stock number/acquisition | IEEE |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA571 |
| Item number | .I37 2016eb |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT |
| Subject category code subdivision | 012000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT012000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT038000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT000000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT034000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT012010 |
| Source | bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 516.3/52 |
| Edition number | 23 |
| 084 ## - OTHER CLASSIFICATION NUMBER | |
| Classification number | SI 830 |
| Number source | rvk |
| 049 ## - LOCAL HOLDINGS (OCLC) | |
| Holding library | MAIN |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Ikromov, Isroil A., |
| Dates associated with a name | 1961- |
| Relator term | author. |
| 9 (RLIN) | 64759 |
| 245 10 - TITLE STATEMENT | |
| Title | Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra / |
| Statement of responsibility, etc. | Isroil A. Ikromov and Detlef M�uller. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Princeton : |
| Name of producer, publisher, distributor, manufacturer | Princeton University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice | [2016] |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Annals of mathematics studies ; |
| Volume/sequential designation | number 194 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc. note | Includes bibliographical references and index. |
| 588 0# - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Print version record. |
| 505 00 - FORMATTED CONTENTS NOTE | |
| Linkage | 880-01 |
| Title | 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 h -- |
| -- | Chapter 7. How to Go beyond the Case h -- |
| -- | 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. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | 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 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 ## - LOCAL NOTE (RLIN) | |
| Local note | IEEE |
| Provenance (VM) [OBSOLETE] | IEEE Xplore Princeton University Press eBooks Library |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Hypersurfaces. |
| 9 (RLIN) | 64760 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Polyhedra. |
| 9 (RLIN) | 64761 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Surfaces, Algebraic. |
| 9 (RLIN) | 64762 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Fourier analysis. |
| 9 (RLIN) | 6642 |
| 650 #2 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Fourier Analysis |
| 9 (RLIN) | 6642 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Hypersurfaces. |
| 9 (RLIN) | 64760 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Poly�edres. |
| 9 (RLIN) | 64763 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Surfaces alg�ebriques. |
| 9 (RLIN) | 64764 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Analyse de Fourier. |
| 9 (RLIN) | 64765 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | polyhedra. |
| Source of heading or term | aat |
| 9 (RLIN) | 64766 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | MATHEMATICS |
| General subdivision | Geometry |
| -- | General. |
| Source of heading or term | bisacsh |
| 9 (RLIN) | 7661 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Fourier analysis. |
| Source of heading or term | fast |
| Authority record control number or standard number | (OCoLC)fst00933401 |
| 9 (RLIN) | 6642 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Hypersurfaces. |
| Source of heading or term | fast |
| Authority record control number or standard number | (OCoLC)fst00965830 |
| 9 (RLIN) | 64760 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Polyhedra. |
| Source of heading or term | fast |
| Authority record control number or standard number | (OCoLC)fst01070511 |
| 9 (RLIN) | 64761 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Surfaces, Algebraic. |
| Source of heading or term | fast |
| Authority record control number or standard number | (OCoLC)fst01139295 |
| 9 (RLIN) | 64762 |
| 655 #0 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 9 (RLIN) | 3294 |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 9 (RLIN) | 3294 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | M�uller, Detlef, |
| Dates associated with a name | 1954- |
| Relator term | author. |
| 9 (RLIN) | 64767 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Ikromov, Isroil A., 1961- |
| Title | Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra. |
| Place, publisher, and date of publication | Princeton : Princeton University Press, [2016] |
| International Standard Book Number | 9780691170541 |
| Record control number | (DLC) 2015041649 |
| -- | (OCoLC)926820349 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Annals of mathematics studies ; |
| Volume/sequential designation | no. 194. |
| 9 (RLIN) | 64768 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ieeexplore.ieee.org/servlet/opac?bknumber=9452407">https://ieeexplore.ieee.org/servlet/opac?bknumber=9452407</a> |
| 880 0# - ALTERNATE GRAPHIC REPRESENTATION | |
| Linkage | 505-01/Grek |
| a | Cover -- 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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