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Fourier and Laplace Transforms

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Organization

  • Lectures (4 SWS)
    • Lecturer: PD Dr. Peter Massopust
    • Module Number: MA5039
    • ECTS-Points: 9
    • Time: Tuesdays and Fridays 14-16
    • Location: MI 02.08.011
  • Exercise Session (2 SWS)
    • Time: Thursdays 14-16
    • Location: MI 00.08.038

Contents

  • Fourier Series
    • Approximation kernels
    • Pointwise convergence
    • Hilbert Transform
    • The Bochner Theorem
  • Fourier Integral
    • Inversion
    • Approximation kernels
    • L^2 Theory
    • Sampling theorems
  • Gabor Transform
  • Laplace Transform

Problem Sets

Problem Set 1

Script

24 April 2017

Literature

  • P. Butzer & R. Nessel, Fourier Analysis and Approximation, Birkhäuser, 1971.
  • K. Chandrasekharan, Classical Fourier Transforms, Springer, 1989.
  • R. Lasser, Introduction to Fourier Series, Marcel Dekker, 1996.
  • W. Rudin, Functional Analysis, McGraw-Hill, 2 ed., 1991.
  • R. Folland, Fourier Analysis and its Applications, American Mathematical Society, 2009.
  • Y. Katznelson, An Introduction to Harmonic Analysis, Cambridge University Press, 2004.