TY  - GEN
AU  - Demeter, Ciprian
TI  - Fourier restriction, decoupling, and applications
SN  - 9781108499705
U1  - 515.2433 
PY  - 2020///
CY  - UK
PB  - Cambridge University Press
KW  - Fourier analysis
KW  - Decoupling--Mathematics
KW  - Abstract Analysis
KW  - Real and Complex Analysis
N2  - 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
ER  -