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.
- Banach spaces and linear operators on Banach spaces.
- L1(RN) space, convolution product,
Fourier transform on L1(RN) 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 L2(RN).
- Fourier series as a unitary transform from L2(Z) to L2([-pi, pi]).
- Schwartz space SN (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.
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.
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: