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Fourier restriction, decoupling, and...

Demeter, Ciprian.

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Fourier restriction, decoupling, and applications

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Fourier restriction, decoupling, and applications/ Ciprian Demeter.
作者:	Demeter, Ciprian.
出版者:	Cambridge :Cambridge University Press, : 2020.,
面頁冊數:	xvi, 331 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 16 Dec 2019).
內容註:	Notation and a few background results -- Linear restriction theory -- Wave packets -- Bilinear restriction theory -- Parabolic rescaling and a bilinear-to-linear reduction -- Kakeya and square function estimates -- Multilinear Kakeya and restriction inequalities -- The Bourgain-Guth method -- The polynomial method -- An introduction to decoupling -- Decoupling for the elliptic paraboloid -- Decoupling for the moment curve -- Decouplings for other manifolds -- Applications of decoupling.
標題:	Fourier analysis. -
電子資源:	https://doi.org/10.1017/9781108584401
ISBN:	9781108584401

Fourier restriction, decoupling, and applications
Demeter, Ciprian.

Fourier restriction, decoupling, and applications[electronic resource] /Ciprian Demeter. - Cambridge :Cambridge University Press,2020. - xvi, 331 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;184. - Cambridge studies in advanced mathematics ;184..

Title from publisher's bibliographic system (viewed on 16 Dec 2019).

Notation and a few background results -- Linear restriction theory -- Wave packets -- Bilinear restriction theory -- Parabolic rescaling and a bilinear-to-linear reduction -- Kakeya and square function estimates -- Multilinear Kakeya and restriction inequalities -- The Bourgain-Guth method -- The polynomial method -- An introduction to decoupling -- Decoupling for the elliptic paraboloid -- Decoupling for the moment curve -- Decouplings for other manifolds -- Applications of decoupling.

The last fifteen years have seen a flurry of exciting developments in Fourier restriction theory, leading to significant new applications in diverse fields. This timely text brings the reader from the classical results to state-of-the-art advances in multilinear restriction theory, the Bourgain-Guth induction on scales and the polynomial method. Also discussed in the second part are decoupling for curved manifolds and a wide variety of applications in geometric analysis, PDEs (Strichartz estimates on tori, local smoothing for the wave equation) and number theory (exponential sum estimates and the proof of the Main Conjecture for Vinogradov's Mean Value Theorem). More than 100 exercises in the text help reinforce these important but often difficult ideas, making it suitable for graduate students as well as specialists. Written by an author at the forefront of the modern theory, this book will be of interest to everybody working in harmonic analysis.

ISBN: 9781108584401Subjects--Topical Terms:

532730
Fourier analysis.

LC Class. No.: QA403.5 / .D46 2020

Dewey Class. No.: 515.2433

Fourier restriction, decoupling, and applications
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505 0 $a Notation and a few background results -- Linear restriction theory -- Wave packets -- Bilinear restriction theory -- Parabolic rescaling and a bilinear-to-linear reduction -- Kakeya and square function estimates -- Multilinear Kakeya and restriction inequalities -- The Bourgain-Guth method -- The polynomial method -- An introduction to decoupling -- Decoupling for the elliptic paraboloid -- Decoupling for the moment curve -- Decouplings for other manifolds -- Applications of decoupling.
520 $a The last fifteen years have seen a flurry of exciting developments in Fourier restriction theory, leading to significant new applications in diverse fields. This timely text brings the reader from the classical results to state-of-the-art advances in multilinear restriction theory, the Bourgain-Guth induction on scales and the polynomial method. Also discussed in the second part are decoupling for curved manifolds and a wide variety of applications in geometric analysis, PDEs (Strichartz estimates on tori, local smoothing for the wave equation) and number theory (exponential sum estimates and the proof of the Main Conjecture for Vinogradov's Mean Value Theorem). More than 100 exercises in the text help reinforce these important but often difficult ideas, making it suitable for graduate students as well as specialists. Written by an author at the forefront of the modern theory, this book will be of interest to everybody working in harmonic analysis.
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