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Course, academic year 2019/2020
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Selected Topics on Functional Analysis (OF) - NRFA175
Title in English: Vybrané partie z funkcionální analýzy (OF)
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Pre-requisite : {Mathematics for physicists I, II}
Incompatibility : NRFA006
Interchangeability : NMMA942
Is incompatible with: NMMA942
Is interchangeable with: NMMA942
Annotation -
Last update: G_M (16.04.2010)
Basic notions of linear functional analysis. Applications of abstract analysis.
Aim of the course -
Last update: G_M (16.04.2010)

An introductory course in functional analysis.

Literature - Czech
Last update: G_M (16.04.2010)

W. Rudin: Analýza v reálném a komplexním oboru, Academia, Praha, 2003

J. Lukeš: Úvod do funkcionální analýzy, skripta MFF

J. Lukeš: Zápisky z funkcionální analýzy, skripta MFF

Teaching methods -
Last update: G_M (16.04.2010)

lecture and exercises

Syllabus -
Last update: G_M (16.04.2010)

1. Linear spaces

algebraic version of Hahn-Banach theorem

2. Hilbert spaces

orthogonal projection; orthogonalization; abstract Fourier series; representation of Hilbert space

3. Normed linear spaces; Banach spaces

bounded linear operators and functionals; Hahn-Banach theorem; dual space; reflexivity; Banach-Steinhaus theorem; open map theorem and closed graph theorem; inverse operator; spectrum of the operator; compact operator; examples of Banach spaces and their duals (integrable functions, continuous functions; Stone-Weierstrass theorem)

4. Locally convex spaces

Hahn-Banach theorem and separation of convex sets; weak convergence; weak topology; extremal point and the Krein-Milman theorem; examples of locally convex spaces (continuous functions, differentiable functions)

 
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