Fourier transforms of measures, fall 2009

Lecturer

Pertti Mattila

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

No lecture on Tuesday, September 29