Zápočet bude udělen za 50% účast a za referát.

Povaha kontroly studia předmětu vylučuje opravné termíny zápočtu.

Credit will be awarded for 50% attendance and a seminar talk.

The nature of the subject rules out possibility of a refer credit exam.

C. Bennett and R. Sharpley: Interpolation of Operators, Academic Press, Princeton, 1988.

L. Pick, A. Kufner, O. John and S. Fučík: Function Spaces I, De Gruyter, Berlin, 2012.

C. Bennett and R. Sharpley: Interpolation of Operators, Academic Press, Princeton, 1988.

L. Pick, A. Kufner, O. John and S. Fučík: Function Spaces I, De Gruyter, Berlin, 2012.

Nové výsledky o funkčních prostorech a jejich aplikacích v teorii interpolací, diferenciálních rovnicích a matematické fyzice.

In the academic year 2018/19 a course A “mild” Theory of Distributions with Applications will be delivered by prof. Feichtinger.

The course will start from the concept of translation invariant linear systems. Each such system turns out the be a “moving average” or equivalently a convolution operator by some linear functon. From this identification one can start to define the convolution of bounded measures (e.g. probability measures, related to random

variables) and even come up with a description of the Fourier Stieltjes transform (up to

the convolution theorem) without making use of Lebesgue integration theory.

3On this basis the short-time Fourier transform (STFT) can be introduced.

It will then be shown how many important con-

cepts (in particular the (generalized) Fourier transform, the kernel theorem, the sprea-

ding representation or the Kohn-Nirenberg symbol of a pseudo-differential operator) can

be explained resp. understood using not yet so familiar function spaces.

New results on function spaces and their applications in theory of interpolation, PDE's and mathematical physics.

Základy teorie míry.

Basic knowledge in measure theory.