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Course unit, curriculum year 2022–2023
MATH.MA.830
Advanced Functional Analysis, 5 cr
Tampere University
- Description
- Completion options
Teaching periods
Active in period 2 (24.10.2022–31.12.2022)
Course code
MATH.MA.830Language of instruction
EnglishAcademic years
2021–2022, 2022–2023, 2023–2024Level of study
Advanced studiesGrading scale
General scale, 0-5Persons responsible
Responsible teacher:
Lassi PaunonenResponsible organisation
Faculty of Information Technology and Communication Sciences 100 %
Coordinating organisation
Computing Sciences Studies 100 %
The course focuses on the theory of unbounded linear operators, especially differential operators, and on analysis of elliptic partial differential equations. In particular, the course introduces the functional analytic tools for the study of existence, regularity properties, and approximation of solutions of elliptic equations.
List of the main topics:
- Closed operators on Banach spaces, definition and characterizations
- Closed-Graph Theorem, Open Mapping Theorem, Uniform Boundedness Principle
- Operator representation of elliptic partial differential equations
- Theory of Sobolev spaces, Sobolev embedding theorems
- Definitions of classical, strong, and weak solutions of elliptic equations
- Existence and regularity of solutions of elliptic equations
- Compact embeddings and spectral representation of differential operators
- The Fourier transform and Fourier multipliers in the analysis of elliptic equations
Learning outcomes
Prerequisites
Compulsory prerequisites
Further information
Learning material
Equivalences
Studies that include this course
Completion option 1
Course completion includes participation in the lecture/problem sessions, weekly submitted preliminary problems, weekly submitted exercise problems, and weekly submitted homework.
Participation in teaching
24.10.2022 – 11.12.2022
Active in period 2 (24.10.2022–31.12.2022)