Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194) / / Isroil A. Ikromov, Detlef Müller.
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 t...
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Ikromov, Isroil A., author. aut http://id.loc.gov/vocabulary/relators/aut Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194) / Isroil A. Ikromov, Detlef Müller. Princeton, NJ : Princeton University Press, [2016] ©2016 1 online resource (272 p.) : 7 line illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 194 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 restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Fourier analysis. Hypersurfaces. Polyhedra. Surfaces, Algebraic. MATHEMATICS / Geometry / General. bisacsh 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. Müller, Detlef, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2016 9783110485103 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2016 9783110485288 ZDB-23-DMA Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2016 9783110638592 print 9780691170541 https://doi.org/10.1515/9781400881246?locatt=mode:legacy https://www.degruyter.com/isbn/9781400881246 Cover https://www.degruyter.com/document/cover/isbn/9781400881246/original |
language |
English |
format |
eBook |
author |
Ikromov, Isroil A., Ikromov, Isroil A., Müller, Detlef, |
spellingShingle |
Ikromov, Isroil A., Ikromov, Isroil A., Müller, Detlef, Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194) / Annals of Mathematics Studies ; 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 |
author_facet |
Ikromov, Isroil A., Ikromov, Isroil A., Müller, Detlef, Müller, Detlef, Müller, Detlef, |
author_variant |
i a i ia iai i a i ia iai d m dm |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
Müller, Detlef, Müller, Detlef, |
author2_variant |
d m dm |
author2_role |
VerfasserIn VerfasserIn |
author_sort |
Ikromov, Isroil A., |
title |
Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194) / |
title_full |
Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194) / Isroil A. Ikromov, Detlef Müller. |
title_fullStr |
Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194) / Isroil A. Ikromov, Detlef Müller. |
title_full_unstemmed |
Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194) / Isroil A. Ikromov, Detlef Müller. |
title_auth |
Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194) / |
title_alt |
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 |
title_new |
Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194) / |
title_sort |
fourier restriction for hypersurfaces in three dimensions and newton polyhedra (am-194) / |
series |
Annals of Mathematics Studies ; |
series2 |
Annals of Mathematics Studies ; |
publisher |
Princeton University Press, |
publishDate |
2016 |
physical |
1 online resource (272 p.) : 7 line illus. Issued also in print. |
contents |
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 |
isbn |
9781400881246 9783110485103 9783110485288 9783110494914 9783110638592 9780691170541 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA571 |
callnumber-sort |
QA 3571 I37 42017 |
url |
https://doi.org/10.1515/9781400881246?locatt=mode:legacy https://www.degruyter.com/isbn/9781400881246 https://www.degruyter.com/document/cover/isbn/9781400881246/original |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
516 - Geometry |
dewey-full |
516.352 |
dewey-sort |
3516.352 |
dewey-raw |
516.352 |
dewey-search |
516.352 |
doi_str_mv |
10.1515/9781400881246?locatt=mode:legacy |
oclc_num |
979882333 |
work_keys_str_mv |
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Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2016 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2016 Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2016 |
is_hierarchy_title |
Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194) / |
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