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Fourier and Laplace Transforms

News

  • The time and room for the exercise session has been changed. The new time is 4:00 - 5:30 PM and the new room is MI 02.10.011.
  • The oral examinations will take place on Monday, July 31, 2017 and Tuesday, Aug 1, 2017. Interested students should sign up for it by writing their name into one of the two lists on my office door.

Organization

  • Lectures (4 SWS)
    • Lecturer: PD Dr. Peter Massopust
    • Module Number: MA5039
    • ECTS-Points: 9
    • Time: Mondays and Wednesdays 12-14
    • Location: MI 02.10.011
  • Exercise Session (2 SWS)
    • Time: Mondays 16-17:30
    • Location: MI 02.10.011

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
Problem Set 2
Problem Set 3
Problem Set 4
Problem Set 5
Problem Set 6
Problem Set 7
Problem Set 8
Problem Set 9
Problem Set 10
Problem Set 11

Script

24 April 2017
26 April 2017
03 May 2017
10 May 2017
12 May 2017
15 May 2017
22 May 2017
24 May 2017
29 May 2017
31 May 2017
07 June 2017
12 June 2017
14 June 2017
19 June 2017
21 June 2017
26 June 2017
28 June 2017
10 July 2017
12 July 2017
17 July 2017
19 July 2017

Literature

  • P. Butzer & R. Nessel, Fourier Analysis and Approximation, Birkhäuser, 1971.
  • K. Chandrasekharan, Classical Fourier Transforms, Springer, 1989.
  • R. Lasser, Fourier and Laplace Transforms, Skript WS 2014/15
  • 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.