Pertti Mattila

Fourier Analysis and Hausdorff Dimension

• Gebundenes Buch

Produktbeschreibung

Modern text examining the interplay between measure theory and Fourier analysis.

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 456
• Erscheinungstermin: 23. Juli 2015
• Englisch
• Abmessung: 235mm x 157mm x 31mm
• Gewicht: 888g
• ISBN-13: 9781107107359
• ISBN-10: 1107107350
• Artikelnr.: 42372802

Autorenporträt

Pertti Mattila is Professor of Mathematics at the University of Helsinki and an expert in geometric measure theory. He has authored the book Geometry of Sets and Measures in Euclidean Spaces as well as more than 80 other scientific publications.

Inhaltsangabe

Preface
Acknowledgements
1. Introduction
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
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
15. Spherical averages and distance sets
16. Proof of the Wolff-Erdöan Theorem
17. Sobolev spaces, Schrödinger equation and spherical averages
18. Generalized projections of Peres and Schlag
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
References
List of basic notation
Author index
Subject index.