Functional Analysis 3

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Advanced parts of functional analysis needed for modern quantum theory.

Requirements:

Basic calculus and linear algebra courses (01MANA, 01MAA2-4, 01LALA, 01LAA2), the first two parts of Functional analysis course (01FAN1, 01FA2).

Syllabus of lectures:

1. Bounded operators in Hilbert spaces, summarization.

2. Topological vector spaces. Schwartz space.

3. Fourier transform.

4. Compact operators.

5. Closed operators, unbounded operators.

6. Symmetric operators, selfadjoint operators.

7. Symmetric extension of symmetric operators. Problem of selfadjoint extensions.

8. Cayley transform.

9. First and Second John von Neumann formula.

Syllabus of tutorials:

1. Summarization of properties of bounded operators on Hilbert spaces.

2. Compact operators.

3. Symmetric, selfadjoint, closed operators. Essential spectrum.

Study Objective:

The goal of study is to finish the basic functional analysis course oriented mainly on modern quantum theory and solving of problems which arise in physical and technical applications.

Study materials:

Key references:

[1] Blank, Exner, Havlíček: Hilbert Space Operators in Quantum Physics, Springer 2008

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Matematické inženýrství (compulsory course of the specialization)