Seminar on Basic Properties of Function Spaces - NMMA347

• Title: Seminář ze základních vlastností prostorů funkcí 1
• Guaranteed by: Department of Mathematical Analysis (32-KMA)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2024
• Semester: winter
• E-Credits: 2
• Hours per week, examination: winter s.:0/2, C [HT]
• Capacity: unlimited
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: taught
• Language: Czech, English
• Teaching methods: full-time
• Is provided by: NMMA457
• Guarantor: prof. RNDr. Luboš Pick, CSc., DSc.; doc. RNDr. Zdeněk Mihula, Ph.D.
• Class: M Bc. OM; M Bc. OM > Doporučené volitelné
• Classification: Mathematics > Functional Analysis

Annotation

English

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: Kaplický Petr, doc. Mgr., Ph.D. (04.06.2019)

Czech

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.

Last update: Kaplický Petr, doc. Mgr., Ph.D. (04.06.2019)

Course completion requirements

English

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: Kaplický Petr, doc. Mgr., Ph.D. (04.06.2019)

Czech

Zápočet bude udělen za 50% účast a za referát.

Povaha kontroly studia předmětu vylučuje opravné termíny zápočtu.

Last update: Kaplický Petr, doc. Mgr., Ph.D. (04.06.2019)

Literature

English

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: Kaplický Petr, doc. Mgr., Ph.D. (04.06.2019)

Syllabus

English

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

Last update: Kaplický Petr, doc. Mgr., Ph.D. (04.06.2019)

Czech

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.

Last update: Kaplický Petr, doc. Mgr., Ph.D. (04.06.2019)

Entry requirements

English

Basic knowledge in measure theory.

Last update: Kaplický Petr, doc. Mgr., Ph.D. (04.06.2019)

Czech

Základy teorie míry.

Last update: Kaplický Petr, doc. Mgr., Ph.D. (04.06.2019)