Fourier analysis and Hausdorff dimension /

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Detalles Bibliográficos
Autor principal: Mattila, Pertti
Formato: Libro
Lenguaje:Inglés
Publicado: Cambridge : Cambridge University Press, c2015
Colección:Cambridge studies in advanced mathematics ; 150
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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