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Opintojakso, lukuvuosi 2021–2022
MATH.MA.810
Introduction to Functional Analysis, 5 op
Tampereen yliopisto
- Kuvaus
- Suoritustavat
Opetusperiodit
Aktiivinen periodissa 1 (1.8.2021–23.10.2021)
Aktiivinen periodissa 4 (7.3.2022–15.5.2022)
Koodi
MATH.MA.810Opetuskieli
EnglishLukuvuodet
2021–2022, 2022–2023, 2023–2024Opintojakson taso
Advanced studiesArvosteluasteikko
General scale, 0-5Vastuuhenkilö
Responsible teacher:
Petteri LaakkonenResponsible teacher:
Lassi PaunonenResponsible organisation
Faculty of Information Technology and Communication Sciences 100 %
Coordinating organisation
Computing Sciences Studies 100 %
The course provides an introduction to the theory of bounded linear operators on general vector spaces, with special emphasis on Banach and Hilbert spaces of functions.
List of the main topics:
- General linear vector spaces, normed spaces and inner product spaces. Completeness and topological aspects. Banach and Hilbert spaces.
- Vector spaces of functions.
- Bounded linear operators on Banach and Hilbert spaces.
- Hahn-Banach Theorem, Riesz Representation Theorem, Minimum Norm Theorem.
- Self-adjoint and compact operators on Hilbert spaces.
- Bases of infinite-dimensional vector spaces.
- 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.
The course in particular provides the mathematical background for the following further courses in mathematical analysis:
- MATH.MA.830 Advanced Functional Analysis
- MATH.APP.810 Mathematical Control Theory
Osaamistavoitteet
Esitietovaatimukset
Pakolliset esitiedot
Lisätiedot
Oppimateriaalit
Vastaavat opintojaksot
Studies that include this course
Suoritustapa 1
Kaikkien osuuksien suorittaminen on pakollista.
Participation in teaching
07.03.2022 – 29.04.2022
Aktiivinen periodissa 4 (7.3.2022–15.5.2022)