You are browsing the curriculum of a past academic year (2020–2021).
Do you want to change to the ongoing academic year?
Course unit, curriculum year 2020–2021
MATH.MA.810
Introduction to Functional Analysis, 5 cr
Tampere University
- Description
- Completion options
Teaching periods
Active in period 3 (1.1.2021–7.3.2021)
Active in period 4 (8.3.2021–31.5.2021)
Course code
MATH.MA.810Language of instruction
EnglishAcademic year
2020–2021Level of study
Advanced studiesGrading scale
General scale, 0-5Persons responsible
Responsible teacher:
Petteri LaakkonenResponsible teacher:
Lassi PaunonenResponsible organisation
Faculty of Information Technology and Communication Sciences 100 %
Core content
- Introduction to metric spaces and their fundamental properties, especially spaces of continuous and integrable functions. Analysis of continuous mappings between two metric spaces. Cauchy-sequences, complete metric spaces and completions. The Banach-Steinhaus fixed point theorem.
- General linear vector spaces and normed spaces. Basics of Banach spaces and the theory of linear operators. Analysis of properties differential equations using operator theory.
- Fundamentals of Hilbert spaces. Operator theory in Hilbert spaces, bounded self-adjoint operators. Minimum norm theorem and the Riesz reperesentation theorem.
- Spectral theory of bounded linear operators. The spectral representation of compact self-adjoint operators.
- Analysis of solvability and solutions of integral equations using operator theory and spectral theory.
Learning outcomes
Prerequisites
Compulsory prerequisites
Recommended prerequisites
Further information
Learning material
Equivalences
Kokonaisuudet, joihin opintojakso kuuluu
Completion option 1
Completion of all options is required.
Participation in teaching
11.01.2021 – 26.02.2021
Active in period 3 (1.1.2021–7.3.2021)