Fourier analysis and Hausdorff dimension /
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Libro |
| Lenguaje: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
c2015
|
| Colección: | Cambridge studies in advanced mathematics ;
150 |
| Materias: | |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
Tabla de Contenidos:
- 1 Introduction
- Part I - Preliminaries and some simpler applications of the Fourier transform
- 2 Measure theoretic preliminaries
- 3 Fourier transforms
- 4 Hausdorff dimension of projections and distance sets
- 5 Exceptional projections and Sobolev dimension
- 6 Slices of measures and intersections with planes
- 7 Intersections of general sets and measures
- Part II - Specific constructions
- 8 Cantor measures
- 9 Bernoulli convolutions
- 10 Projections of the four-corner Cantor set
- 11 Besicovitch sets
- 12 Brownian motion
- 13 Riesz products
- 14 Oscillatory integrals (stationary phase) and surface measures
- Part III - Deeper applications of the Fourier transform
- 15 Spherical averages and distance sets
- 16 Proof of the Wolff–Erdoğan Theorem
- 17 Sobolev spaces, Schrödinger equation and spherical averages
- 18 Generalized projections of Peres and Schlag
- Part IV - Fourier restriction and Kakeya type problems
- 19 Restriction problems
- 20 Stationary phase and restriction
- 21 Fourier multipliers
- 22 Kakeya problems
- 23 Dimension of Besicovitch sets and Kakeya maximal inequalities
- 24 (n, k) Besicovitch sets
- 25 Bilinear restriction