Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-65-14-K-7

Distributions and Wavelets (2V, 4.5 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
2 V Lecture 4.5 CP 28 h 107 h
(2V) 4.5 CP 28 h 107 h

Basedata

SWS 2V
CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-SPAS] Analysis and Stochastics
Livecycle-State [NORM] Active

Contents

  • test functions and distributions,
  • operations on distributions (translation, dilation, differentiation, folding),
  • Schwartz functions and tempered distributions,
  • Fourier transformations of tempered distributions,
  • wavelets and wavelet frames.

Literature

  • W. Walter: Einführung in die Theorie der Distributionen,
  • I. M. Gelfang, G. E. Schilow: Verallgemeinerte Funktionen I,
  • W. Rudin: Functional Analysis,
  • R. Strichartz: A Guide to Distribution Theory and Fourier Transform,
  • G. B. Folland: Fourier Analysis and its Applications,
  • I. Daubechies: Ten Lectures on Wavelets,
  • S. Mallat: A Wavelet Tour of Signal Processing.

Materials

Further literature will be announced in the lecture.

Requirements for attendance (informal)

Knowledge in the field of image processing (e.g. from the module [MAT-65-11-M-7]) is helpful, but not necessarily required.

Modules:

Courses

Requirements for attendance (formal)

None

References to Course [MAT-65-14-K-7]

Module Name Context
[MAT-65-14-M-7] Distributions and Wavelets P: Obligatory 2V, 4.5 LP