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Course, academic year 2019/2020
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Harmonic Analysis 2 - NMAG534
Title in English: Harmonická analýza 2
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019 to 2019
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:3/1 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: not taught
Language: Czech, English
Teaching methods: full-time
Guarantor: doc. RNDr. Svatopluk Krýsl, Ph.D.
Class: M Mgr. MSTR
M Mgr. MSTR > Povinně volitelné
Classification: Mathematics > Geometry
Annotation -
Last update: T_MUUK (13.05.2015)
Harmonic analysis generalizes the classical Fourier analysis of partial differential equations in R^n for other groups than the abelian R^n. Second part of lecture.
Aim of the course -
Last update: T_MUUK (13.05.2015)

Study of non-commutative analysis.

Course completion requirements -
Last update: doc. RNDr. Svatopluk Krýsl, Ph.D. (22.02.2019)

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

The exam is oral with a written preparation.

Credit is given for active participation, proving easy theorems or computing examples

in harmonic analysis. Credit is not necessary for doing the exam.

Literature -
Last update: doc. RNDr. Svatopluk Krýsl, Ph.D. (22.02.2019)

Goodman, R., Walach, N., Invariants and Representations of Classical Groups, Oxford

Knapp, A., Representation theory of semi-simple Lie groups: An overview based on examples, Princeton

Kirillov, A., Representation theory and Noncommutative Harmonic Analysis I, II, Springer

Dixmier, J., Envelopping Algebras, AMS

Sepanski, M., Compact Lie groups, Springer

Teaching methods -
Last update: T_MUUK (13.05.2015)

Lecture and exercise.

Requirements to the exam -
Last update: doc. RNDr. Svatopluk Krýsl, Ph.D. (22.02.2019)

We test definitions and theorems and its application in clearly arranged situations.

Syllabus -
Last update: doc. RNDr. Svatopluk Krýsl, Ph.D. (28.06.2017)

1) Recall and deepen of Highest weight theory (theorem of Poincare-Birkhoff-Witt, Verma modulues)

2) Recall and deepen of Invariants of classical groups (Schur-Weyl duality - Young diagrams, harmonic polynomials)

3) Theorem of Borel-Bott-Weil

4) Unitary dual of SL(2,R) and SL(2,C)

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