*This course is not currently conducted!*

*Erasmus code:*11.1

*ISCED code:*0541

*ECTS credits:*unknown

*Language:*Polish

*Organized by:*Faculty of Physics

*Related to study programmes:*

# Functional Analysis I 1100-2Ind10

The aim of the course is to provide necessary knowledge concerning the basic mathematical structures needed in studying theoretical physics.

**Program:**

- Banach spaces and linear operators on Banach spaces.

- L^{1}(R^{N}) space, convolution product,

Fourier transform on L^{1}(R^{N}) and its properties.

- Hilbert space and its properties, basic classes of linear operators

(isometries, unitaries, self-adjoint operators).

- General theory of orthogonal polynomials.

- Fourier transform on L^{2}(R^{N}).

- Fourier series as a unitary transform from L^{2}(Z) to L^{2}([-pi, pi]).

- Schwartz space S_{N} (bi-algebra structure, topology), Fourier transform on Schwartz space and its properties.

- Distribution (generalized functions) and their properties,

basic operations (differentation, convolution product problem).

- Tempered distributions, Fourier transform of tempered distribution.

- Support of distribution, distributions with compact support.

Student's work load: 140 h includes

Lectures and classes: 60 h

Preparation for lectures: 45 h

Preparation for the exam: 35 h

Description by Wiesław Pusz, November 2010.

## Mode

## Prerequisites (description)

## Learning outcomes

Knowledge: Familiarity with basic theory of distributions and Hilbert spaces.

Skills: Use of distributions and Fourier transform in equations of mathematical physics

Attitude: Appreciation of the beauty, depth and usefulness

of Hilert spaces and distributions especially in the context of applications to physics.

## Additional information

Information on *level* of this course, *year of study* and semester when the course
unit is delivered, types and amount of *class hours* - can be found in course structure
diagrams of apropriate study programmes. This course is related to
the following study programmes:

Additional information (*registration* calendar, class conductors,
*localization and schedules* of classes), might be available in the USOSweb system: