Institute of Applied Mathematics
Lecture in Summer Term 2022
Elective subject mathematics (Analysis)
Content
The lecture will deal with the theory of distributions and some aspects of Fourier analysis. The covered topics include: Test functions and distributions Tensor product and convolution of distributions Schwartz space and tempered distributions Distributional Fourier and Laplace transform Gelfand-Shilov spaces
Lecture
Dr. Petr Siegl The schedule for the lecture can be found in the TUGonline
Textbooks
Friedlander, F. G. Introduction to the theory of distributions, second ed. Cambridge University Press, Cambridge, 1998. With additional material by M. Joshi Gelfand, I. M., and Shilov, G. E. Generalized functions 1: Properties and operations, vol. 1. AMS Chelsea Publishing, Providence, RI, 2016 Gelfand, I. M., and Shilov, G. E. Generalized Functions 2: Spaces of Fundamental and Generalized Functions, vol. 2. AMS Chelsea Publishing, Providence, RI, 2016 Vladimirov, V. S. Equations of mathematical physics. Marcel Dekker, Inc., New York, 1971 Vladimirov, V. S. Methods of the theory of generalized functions. Taylor & Francis, London, 2002