Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra:
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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| Beteiligte Personen: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[2016]
|
| Schriftenreihe: | Annals of Mathematics Studies
number 194 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1515/9781400881246?locatt=mode:legacy https://doi.org/10.1515/9781400881246?locatt=mode:legacy https://doi.org/10.1515/9781400881246?locatt=mode:legacy https://doi.org/10.1515/9781400881246?locatt=mode:legacy https://doi.org/10.1515/9781400881246?locatt=mode:legacy https://doi.org/10.1515/9781400881246?locatt=mode:legacy http://doi.org/10.1515/9781400881246?locatt=mode:legacy https://doi.org/10.1515/9781400881246?locatt=mode:legacy https://doi.org/10.1515/9781400881246 |
| Zusammenfassung: | 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 |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed Oct. 27, 2016) |
| Umfang: | 1 online resource |
| ISBN: | 9781400881246 |
| DOI: | 10.1515/9781400881246 |
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| 520 | |a 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 | ||
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| id | DE-604.BV043979302 |
| illustrated | Not Illustrated |
| indexdate | 2025-02-18T15:09:59Z |
| institution | BVB |
| isbn | 9781400881246 |
| language | English |
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| publishDate | 2016 |
| publishDateSearch | 2016 |
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| publisher | Princeton University Press |
| record_format | marc |
| series | Annals of Mathematics Studies |
| series2 | Annals of Mathematics Studies |
| spellingShingle | Ikromov, Isroil A. 1961- Müller, Detlef 1954- Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra Annals of Mathematics Studies Fourier analysis Hypersurfaces Polyhedra Surfaces, Algebraic |
| title | Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra |
| title_auth | Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra |
| title_exact_search | Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra |
| title_full | Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra Isroil A. Ikromov, Detlef Müller |
| title_fullStr | Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra Isroil A. Ikromov, Detlef Müller |
| title_full_unstemmed | Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra Isroil A. Ikromov, Detlef Müller |
| title_short | Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra |
| title_sort | fourier restriction for hypersurfaces in three dimensions and newton polyhedra |
| topic | Fourier analysis Hypersurfaces Polyhedra Surfaces, Algebraic |
| topic_facet | Fourier analysis Hypersurfaces Polyhedra Surfaces, Algebraic |
| url | https://doi.org/10.1515/9781400881246 |
| volume_link | (DE-604)BV040389493 |
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