Functional Analysis/Funktionalanalys TVM0025

Third-cycle course

COURSE SYLLABUS, third-cycle courses

Course name: Functional Analysis/Funktionalanalys

ECTS/HP: 7,5

Course code: TVM0025

Educational level: Third-cycle course

Entry requirements

Undergraduate calculus and linear algebra, for example Differential calculus (M0047M), Linear algebra and Calculus (M0048), Linear algebra and Differential Equations (M0049M), Multivariable Calculus (M0055M) or their equivalents. Principles of Mathematical Analysis (M7026) or an equivalent is recommended.

Course content and learning outcomes

Metric, normed and inner product spaces. Bounded operators. Dual spaces. The Hahn-Banach theorem, the Banach-Steinhaus theorem, open mapping theorem and the closed graph theorem. Strong and weak topology. Spectral theory. Fixed-point theorems with applications.

After completed course, the students should be able to:

• define and carefully explain topological properties for different kinds of metric spaces.
• define and carefully explain for Banach and Hilbert spaces.
• formulate and prove basic theorems as the Hahn-Banach theorem, open mapping theorem, the Banach-Steinhaus theorem and the closed graph theorem.
• be able to use and apply central concepts within the course such as reflexivity, strong and weak topology, linear operators, adjoint operators and compact operators.
• account for some fixed-point theorems.
• account for basic spectral theory.

Course methods
Self-study with guidance. Examination tasks.

Examination form
Examination tasks.

Grading scale: Pass/Fail

Course literature
Kreyzsig E.: Introductory Functional Analysis with Applications. John Wiley 1978

Education cycle: Third-cycle, January 15, 2024 – May 31, 2024.

Course is given periodically: Yes, 2025 tentatively.

Send application to: Stefan Ericsson, sen@ltu.se.

Deadline for application: January 1, 2024

Course open for application by doctoral students admitted to other universities than LTU: Yes

Limited number of students: No limit

Tuition
No fee for university employed PhD students

Contact person
Stefan Ericsson, sen@ltu.se, 0920-493330

Examiner
Prof. Peter Wall

Course syllabus decided by: Prof. Lars-Göran Westerberg, Director for PhD studies
Date of decision: 2023-11-08