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Fourier restriction, decoupling, and applications / Ciprian Demeter.
Math/Physics/Astronomy - Reserve QA403.5 .D46 2020
Available
Log in to request item- Format:
- Book
- Author/Creator:
- Demeter, Ciprian, author.
- Series:
- Cambridge studies in advanced mathematics ; 184.
- Cambridge studies in advanced mathematics ; 184
- Language:
- English
- Subjects (All):
- Fourier analysis.
- Decoupling (Mathematics).
- Physical Description:
- xvi, 331 pages ; 24 cm.
- Place of Publication:
- Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2020.
- Summary:
- "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"-- Provided by publisher.
- Contents:
- 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.
- Notes:
- Includes bibliographical references and index.
- Other Format:
- Online version: Demeter, Ciprian. Fourier restriction, decoupling and applications.
- ISBN:
- 9781108499705
- 1108499708
- OCLC:
- 1135907826
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