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Elements of the Theory of Distributions

News

  • The oral examinations will take place on August 6 and 7, 2019, in my office (MI 02.08.040). If you are interested in taking the exam, enter your name in one of the lists on my office door.
  • The exercise sessions will begin on Thursday, May 16, 2019. They will take place every other week from 2-4 PM in room MI 00.09.022.

Organization

  • Lectures (2 SWS)
    • Lecturer: PD Dr. Peter Massopust
    • Module Number: MA5319
    • ECTS-Points: 5
    • Time: Wednesdays 12-14
    • Location: MI 03.10.011
  • Exercise Session (1 SWS)
    • Time: 2 - 4 PM (every other week)
    • Location: 00.09.022

Contents

  • Test Functions
  • Dirac Delta Distribution
  • Distributions on D
  • Distributions on S
  • Convolution of Distributions
  • Derivatives and the Fourier Transform of Distributions
  • Ultradistributions

Problem Sets

Current Script

Script

Literature

  • R. Brigola: Fourieranalysis, Distributionen, und Anwendungen, Vieweg 1997 (basic)
  • K. Burg, H. Haf, F. Wille, A. Meister: Höhere Mathematik für Ingenieure, Band III, 6. Auflage, Springer Verlag 2013 (basic)
  • I. Richards & H. Youn: The Theory of Distributions, Cambridge University Press, 1995 (basic)
  • M. J. Lighthill: An Introduction to Fourier Analysis and Generalised Functions, Cambridge University Press, 1964 (basic)
  • D. Müller-Wichards: Transformationen und Signale, 2. Auflage, Springer Verlag, 2013 (basic)
  • W. Walter: Einführung in the Theorie der Distributionen, Bibliographisches Institut, Mannheim, 1970 (advanced)
  • E. Berz: Verallgemeinerte Funktionen und Operatoren, B.I. Hochschultaschenbücher, 122/122a, Mannheim 1967 (advanced)
  • A. H. Zemanian: Distribution Theory and Transform Analysis, Dover, New York, 1967 (advanced)
  • L. Schwartz: Théorie des distributions, Hermann, Paris 1978 (advanced)
  • I. Gel'fand & G. Shilov: Generalized Functions, Vol. 1, AMS, 2016 (advanced)