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Course, academic year 2024/2025
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Mathematical Analysis Elective 2 - NMMA499 (Fourier analysis on commutative groups)
Title: Výběrová přednáška Matematická analýza 2
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech
Teaching methods: full-time
Note: you can enroll for the course repeatedly
Class: M Mgr. MA
M Mgr. MA > Volitelné
Classification: Mathematics > Real and Complex Analysis
Annotation -
Non-repeated universal elective course. 2020-21: Fourier analysis on groups generalizes theory of Fourier series and Fourier transform on R^n.
Last update: Kaplický Petr, doc. Mgr., Ph.D. (02.07.2020)
Aim of the course -

Study of Fourier analysis for locally compact commutative groups.

Last update: Kaplický Petr, doc. Mgr., Ph.D. (02.07.2020)
Course completion requirements -

The course is finished by an oral exam.

Last update: Kaplický Petr, doc. Mgr., Ph.D. (02.07.2020)
Literature

W. Rudin - Fourier analysis on groups

Last update: Kaplický Petr, doc. Mgr., Ph.D. (02.07.2020)
Requirements to the exam -

We test the knowledge of definitions, theorems and their application.

Last update: Kaplický Petr, doc. Mgr., Ph.D. (02.07.2020)
Syllabus -

Topological groups, Haar measure, convolutions, L_1(G) as a Banach algebra, dual group, Fourier transform, Bochner and Plancherel theorem, Pontryagin duality.

Last update: Kaplický Petr, doc. Mgr., Ph.D. (02.07.2020)
Entry requirements - Czech

Přednáška navazuje na některé znalosti z Funkcionální analýzy 1.

Last update: Spurný Jiří, prof. RNDr., Ph.D., DSc. (03.07.2020)
 
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