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Fourier Analysis/

Number of credits: 8 hp

Examiner: Bengt Ove Turesson

Course literature: Lecture notes (handed out during the course), literature references on the course homepage

Course contents:

  • Fourier series: Revision, convergence tests, integration, Riemann's localization principle, Gibbs' phenomenon, absolutely convergent series, summability of Fourier series, divergence of Fourier series, the Poisson summation formula
  • The Fourier transform: Revision, multi-dimensional theory, inversion, interpolation, the Shannon sampling theorem
  • Distribution theory: Revision, the Paley-Wiener theorem, the Fourier-Laplace transform, homogeneous distributions, fundamental solutions, micro-local analysis
  • Wavelets: Revision, Riesz bases, frames, function spaces

Organisation: Lectures

Examination: Assignments

Prerequisites: TATA26 Fourier analysis, TATA66 Fourier and Wavelet Analysis, TATM85 Functional Analysis or equivalent courses

Sidansvarig: karin.johansson@liu.se
Senast uppdaterad: 2015-09-15