Comprehensive coverage of recent, exciting developments in Fourier restriction theory, including applications to number theory and PDEs.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Ciprian Demeter is Professor of Mathematics at Indiana University, Bloomington. He is one of the world's leading experts in Fourier restriction theory and its applications to number theory, which he teaches regularly at the graduate level. He received the Sloan fellowship in 2009 and was an invited speaker at the 2018 International Congress of Mathematicians in Rio de Janeiro.
Inhaltsangabe
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.
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.
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