Lecture: Fourier Restriction and Applications (SS 2025)

1. C. Demeter - Fourier Restriction, Decoupling, and Applications
2. L. Grafakos - Classical Fourier Analysis (available online)
3. P. Mattila - Fourier Analysis and Hausdorff Dimension
4. C.D. Sogge - Fourier Integrals in Classical Analysis
5. C.D. Sogge - Hangzhou Lectures on Eigenfunctions of the Laplacian
6. E. M. Stein - Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals (available online)
7. T. Tao - Notes on Fourier analysis
8. T. Tao - Topics in real analysis: restriction theorems, Besicovitch sets, and applications to PDE
9. T. Tao - Recent progress on the restriction conjecture
10. R. Vershynin - High-Dimensional Probability
11. T. Wolff - Lectures in Harmonic Analysis (available online)
12. D. R. Yafaev - Mathematical Scattering Theory. Analytic Theory

1. Crumbly notes
2. More on the locally constant lemma, wave packet decomposition
3. More precise estimates for Bessel functions can be found here, in Barcelo-Ruiz-Vega, and in Cordoba
4. Sharp Tomas-Stein Fourier restriction with vanishing curvatures in three dimensions was carried out by Ikromov and Müller
5. For more general versions and an optimal extension of the Tomas-Stein theorem to Lorentz spaces, see Bak and Seeger
6. References for randomized restriction theorems: dual to Sudakov by Pajor-Tomczak--Jaegermann and Bourgain-Lindenstrauss-Milman. Random trace lemma by Bourgain and random Tomas-Stein by Bourgain