Last update: doc. Mgr. Petr Kaplický, Ph.D. (01.06.2017)
Seminar third year bachelor students. Seminar covers basic properties of spaces containing integrable,
differentiable and smooth functions and operators acting on such
spaces.
Last update: doc. Mgr. Petr Kaplický, Ph.D. (23.05.2018)
Doporučený volitelný seminář pro bakalářský obor Obecná matematika. Seminář zahrnující základní vlastnosti
prostorů integrovatelných, diferencovatelných a hladkých funkcí a vlastnosti operátorů na těchto prostorech. Je
vhodný pro studenty magisterského a doktorského studia, jakož i studenty 3. ročníku bakalářského studia. Seminář
lze zapsat opakovaně.
Course completion requirements -
Last update: prof. RNDr. Luboš Pick, CSc., DSc. (22.07.2018)
Credit will be awarded for 50% attendance and a seminar talk.
The nature of the subject rules out possibility of a refer credit exam.
Last update: prof. RNDr. Luboš Pick, CSc., DSc. (22.07.2018)
Zápočet bude udělen za 50% účast a za referát.
Povaha kontroly studia předmětu vylučuje opravné termíny zápočtu.
Literature -
Last update: prof. RNDr. Luboš Pick, CSc., DSc. (22.07.2018)
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.
Last update: prof. RNDr. Luboš Pick, CSc., DSc. (22.07.2018)
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.
Syllabus -
Last update: doc. Mgr. Petr Kaplický, Ph.D. (01.06.2017)
New results on function spaces and their applications in theory of interpolation, PDE's and mathematical physics.
Last update: doc. Mgr. Petr Kaplický, Ph.D. (23.05.2018)
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.
Entry requirements -
Last update: prof. RNDr. Luboš Pick, CSc., DSc. (22.07.2018)
Basic knowledge in measure theory.
Last update: prof. RNDr. Luboš Pick, CSc., DSc. (22.07.2018)