Czech

Not applicable.

Knowledge of basic topics of Fourier Analysis, manely, Fourier series, Fourier and Laplace transformations, and ability to apply this knowledge in practice.

Calculus, basic konwledge of linear functional analysis, measure theory.

Not applicable.

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Participation in the seminars is mandatory.
Course-unit credit is awarded on condition of having attended the seminars actively and passed the control test.
Examination has a practical and a theoretical part. In the practical part student has to illustrate the given tasks on particular examples.
Theoretical part includes questions related to the subject-matter presented at the lectures.

1. Space of integrable functions - definition and basic properties, dense subsets,
convergence theorems.
2. Space of quadratically integrable functions - different kinds of convergence, Fourier series.
3. Singular integral - definition, representation, application to Fourier series.
4. Trigonometric series.
5. Fourier integral.
6. Fourier transformation - Fourier transformation (FT), inverse formula, basic properties of FT, Hermit and Laguer functions, FT and convolution, applications.
7. Plancherel theorem, Hermit functions.
8. Laplace transformation.

Not applicable.

The aim of the course is to familiarise students with basic topics and techniques of the Fourier analysis used in other mathematical subjects

Absence has to be made up by self-study using recommended literature.

Not applicable.

Not applicable.

A. N. Kolmogorov, S. V. Fomin: Základy teorie funkcí a funkcionální analýzy, SNTL, Praha 1975. (CS)
E. M. Stein´, G. Weiss: Introduction to Fourier Analysis on Eucledian spaces, Princeton University Press, 1971. (EN)
E. W. Howel, B. Keneth: Principles of Fourier Analysis, CRC Press, 2001. (EN)
I. P. Natanson: Teorija funkcij veščestvennoj peremennoj, [Theory of functions of a real variable] ,Third edition, "Nauka'', Moscow, 1974. (RU)

Not applicable.