Fourier Restriction, Decoupling, and Applications

ISBN-13: 9781108499705 / Angielski / Twarda / 2020 / 345 str.

Ciprian Demeter

Opis

Recent years have seen a flurry of advances in Fourier restriction theory, with significant applications in number theory, PDEs and geometric analysis. This timely text for specialists and graduate students in analysis, written by a leader in the field, brings the reader to the forefront of these exciting developments.

Recenzje

'Undoubtedly, this book will become an indispensable reference in the subject.' Pablo Alejandro Rocha, European Mathematical Society

Spis treści

Background and notation; 1. Linear restriction theory; 2. Wave packets; 3. Bilinear restriction theory; 4. Parabolic rescaling and a bilinear-to-linear reduction; 5. Kakeya and square function estimates; 6. Multilinear Kakeya and restriction inequalities; 7. The Bourgain–Guth method; 8. The polynomial method; 9. An introduction to decoupling; 10. Decoupling for the elliptic paraboloid; 11. Decoupling for the moment curve; 12. Decouplings for other manifolds; 13. Applications of decoupling; References; Index.