Fourier transforms of measures, fall 2009
Last modified by pemattil@helsinki_fi on 2024/03/27 09:58
Fourier transforms of measures, fall 2009
Lecturer
Scope
10 cu.
Type
Advanced studies.
Prerequisites
Basic knowledge of measure and integration and real analysis. For example the courses mitta ja integraali and reaalianalyysi I are sufficient, but also reaalianalyysi II would be useful. Knowledge of Fourier analysis is not necessary but would be helpful.
Lectures
Weeks 39-43 and 45-51, Tuesday 10-12 and Thursday 10-12 in room C123.
Content
Some of the topics included will be
- relations between Fourier transform and Hausdorff dimension
- applications of Fourier transform to Hausdorff dimension
- Fourier transforms of Cantor-type measures
- Fourier transform and Brownian motion
Bibliography
There is no course book. Some parts of the course can be found in
- P. Mattila, Geometry of Sets and Measures in Euclidean Spaces
- Th.Wolff, Lectures on Harmonic Analysis