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Modul
Harmonic Analysis on Fractals [M-MATH-106287]
Credits
3Recurrence
EinmaligDuration
1 SemesterLanguage
EnglishLevel
4Version
1Responsible
Organisation
- KIT-Fakultät für Mathematik
Part of
Bricks
Identifier | Name | LP |
---|---|---|
T-MATH-112742 | Harmonic Analysis on Fractals | 3 |
Competence Goal
After the course, students will be able to discuss
- examples of fractals and their properties,
- different notions of fractal dimension and their relationships,
- the interaction between metric and harmonic-analytic properties of fractals,
- selected recent developments in the harmonic analysis of fractals.
Prerequisites
none
Content
This course aims to be an accessible introduction to fractals and
selected aspects of their modern harmonic-analytic theory.
We first introduce examples of fractals and their dimension theory:
- fractals in nature, Cantor sets and Bernoulli convolutions,
number-theoretic fractals, Brownian motion, Kakeya sets, - Hausdorff dimension, box dimension and intermediate dimensions,
- Fourier transforms of measures and Fourier dimension.
Then we study topics of recent research interest in harmonic analysis:
- Fourier restriction theorems on fractals,
- fractal uncertainty principles.
Recommendation
Some basic knowledge of functional analysis is recommended.