Functional Analysis 1

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Continuing course of mathematical analysis and algebra introduction to the basics of functional analysis. There are the concepts that students need to understand the various physical and technical disciplines.

Requirements:

Basic course of Calculus and Linear Algebra (in the extent of the courses 01MA, 01MAA2-4, 01LAP, 01LAA2 held at the FNSPE CTU in Prague).

Syllabus of lectures:

1. Vector spaces 2. Metric and topological spaces 3.Topological vector spaces 4.Banach spaces 5.Bounded linear mappings 6. Fourier-Plancherel operator, Fourier transformation 7. Spectrum of closed linear operators 8.Hermitean operators, Projectors 9.Unitary and isometrical operators 10.Spectral properties of normal operators 11.Ideal of the compact operators 12. Spectrum of compact operators

Syllabus of tutorials:

Exercise is closely linked to the lecture, which is illustrated by appropriate examples. Accent is placed on the correctness of the calculation.

Study Objective:

Complete mathematical education of our graduates oriented research.

Study materials:

Key references: J.Blank.P,Exner,M.Havlíček: Hilbert Space Operators in Quantum Physics, Springer,2008.

Recommended references: M. Reed, B. Simon : Methods of Modern Mathematical Physics I.-IV. ACADEMIC PRESS, N.Z. 1972-1979.

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Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: