Fourier transforms of measures, fall 2009
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.
Weeks 39-43 and 45-51, Tuesday 10-12 and Thursday 10-12 in room C123.
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
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