Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra

AvIsroil A. Ikromov,Detlef Müller

Inbunden, Engelska, 2016

Del i serien Annals of Mathematics Studies

1 833 kr

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Häftad

839 kr

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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 Muller 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 Muller 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.

Produktinformation

Utgivningsdatum:2016-05-24
Mått:152 x 235 x 20 mm
Vikt:522 g
Format:Inbunden
Språk:Engelska
Serie:Annals of Mathematics Studies
Antal sidor:272
Förlag:Princeton University Press
ISBN:9780691170541

Utforska kategorier

Mer om författaren

Isroil A. Ikromov is professor of mathematics at Samarkand State University in Uzbekistan. Detlef Muller is professor of mathematics at the University of Kiel in Germany.

Innehållsförteckning

*Frontmatter, pg. i*Contents, pg. vii*Chapter 1. Introduction, pg. 1*Chapter 2. Auxiliary Results, pg. 29*Chapter 3. Reduction to Restriction Estimates near the Principal Root Jet, pg. 50*Chapter 4. Restriction for Surfaces with Linear Height below 2, pg. 57*Chapter 5. Improved Estimates by Means of Airy-Type Analysis, pg. 75*Chapter 6. The Case When hlin(PHI) => 2: Preparatory Results, pg. 105*Chapter 7. How to Go beyond the Case hlin(PHI) => 5, pg. 131*Chapter 8. The Remaining Cases Where m = 2 and B = 3 or B = 4, pg. 181*Chapter 9. Proofs of Propositions 1.7 and 1.17, pg. 244*Bibliography, pg. 251*Index, pg. 257

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Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra

AvIsroil A. Ikromov,Detlef Müller

Inbunden, Engelska, 2016

Del i serien Annals of Mathematics Studies

1 833 kr

Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt över 249 kr.

Fler format och utgåvor

Häftad

839 kr

Beskrivning

Produktinformation

Utgivningsdatum:2016-05-24
Mått:152 x 235 x 20 mm
Vikt:522 g
Format:Inbunden
Språk:Engelska
Serie:Annals of Mathematics Studies
Antal sidor:272
Förlag:Princeton University Press
ISBN:9780691170541

Utforska kategorier

Mer om författaren

Isroil A. Ikromov is professor of mathematics at Samarkand State University in Uzbekistan. Detlef Muller is professor of mathematics at the University of Kiel in Germany.

Innehållsförteckning

*Frontmatter, pg. i*Contents, pg. vii*Chapter 1. Introduction, pg. 1*Chapter 2. Auxiliary Results, pg. 29*Chapter 3. Reduction to Restriction Estimates near the Principal Root Jet, pg. 50*Chapter 4. Restriction for Surfaces with Linear Height below 2, pg. 57*Chapter 5. Improved Estimates by Means of Airy-Type Analysis, pg. 75*Chapter 6. The Case When hlin(PHI) => 2: Preparatory Results, pg. 105*Chapter 7. How to Go beyond the Case hlin(PHI) => 5, pg. 131*Chapter 8. The Remaining Cases Where m = 2 and B = 3 or B = 4, pg. 181*Chapter 9. Proofs of Propositions 1.7 and 1.17, pg. 244*Bibliography, pg. 251*Index, pg. 257