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Fourier transforms of measures, fall 2009


Pertti Mattila


10 cu.


Advanced studies.


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

No lecture on Tuesday, September 29

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