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Harmonic Analysis

MA5954Elective Modules3 ECTSEnglishEinmaligDepartment Mathematics
AI-edited module sheet. Based on the TUMonline module description, edited for readability.Original in TUMonline

What it is about

You will learn core techniques of harmonic analysis such as Fourier transformation, singular integrals and function spaces. In the end you will be able to apply these methods to the study of partial differential equations, in the theory of function spaces and in applications such as signal processing.

What you will be able to do

  • Understanding of Fourier transformation and convolution
  • Mastery of the Hardy-Littlewood maximal operator and interpolation theory
  • Use of the Hilbert transform and knowledge of BMO
  • Application of Calderón-Zygmund theory for singular integrals
  • Familiarity with Littlewood-Paley theory and Hörmander multiplier theorems
  • Insight into Sobolev-, Besov- and Triebel-Lizorkin spaces
  • Knowledge of probabilistic tools such as Khintchine inequalities

What the module consists of

  • LectureThe contents are presented and discussed in lectures with demonstrative examples.

Teaching method

  • Lecture with examplesPresentation of the theory and demonstration of typical examples
  • DiscussionInteractive discussion of the topics and encouragement of independent deepening
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Official page in TUMonline · Details are not binding.