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Opintojakso, lukuvuosi 2021–2022
MATH.MA.810

Introduction to Functional Analysis, 5 op

Tampereen yliopisto
Opetusperiodit
Aktiivinen periodissa 1 (1.8.2021–23.10.2021)
Aktiivinen periodissa 4 (7.3.2022–15.5.2022)
Koodi
MATH.MA.810
Opetuskieli
English
Lukuvuodet
2021–2022, 2022–2023, 2023–2024
Opintojakson taso
Advanced studies
Arvosteluasteikko
General scale, 0-5
Vastuuhenkilö
Responsible teacher:
Petteri Laakkonen
Responsible teacher:
Lassi Paunonen
Responsible 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.

Exam

07.09.2021 07.09.2021
Aktiivinen periodissa 1 (1.8.2021–23.10.2021)
10.05.2022 10.05.2022
Aktiivinen periodissa 4 (7.3.2022–15.5.2022)

Participation in teaching

07.03.2022 29.04.2022
Aktiivinen periodissa 4 (7.3.2022–15.5.2022)