The course will follow the lecture notes "Funktonaalianalyysin peruskurssi" (2012, last updated in 2017) by Kari Astala, Petteri Piiroinen & Hans-Olav Tylli. Minor updates are possible also during the course and the most current version for the Autumn 2018 course can be downloaded from below.
* The notes are available only in Finnish but an English textbook substitute, which is particularly suitable for those who wish to focus on applications, is
Erwin Kreyszig: Introductory functional analysis with applications (Wiley, 1989)
* Although perhaps not optimal as a textbook, a concise but solid reference book including also material for the courses Real Analysis I and Complex Analysis I is
W. Rudin: Real and Complex Analysis (Tata McGraw-Hill) [chapters 3-5 summarize the main material for this course]
* The following books contain related material (as well as much more), and may be used as supplement to the course notes/textbook:
Bollobas: Linear Analysis (Cambridge Mathematical Textbooks)
Werner: Funktionalanalysis (Springer-Lehrbuch) [in German]
W. Rudin: Functional Analysis (McGraw-Hill) [Part I generalizes the theory to topological vector spaces]
Homework sets, second period
The exercise sessions will be on Thursdays 14:15-16:00 in Exactum, C129, on the date marked at the top of the exercise sheet. You can either come to present your solutions in the session, or contact the instructor Kalle Koskinen (email@example.com) to make alternative arrangements if you cannot attend it.
Please make free use of the Ratkomo -tutorial sessions on the 3rd floor: the schedule is available at the web page https://blogs.helsinki.fi/ratkomo-solvery/aikataulu-timetable/ As mentioned during the lectures, the lecturer and/or instructor are often also answering questions in Ratkomo on Tuesdays between 13-15. In particular, you are welcome to ask questions from the lecturer during the office hours on Tue 14-15 at Exactum D335.
Solutions, second period
Homework sets, first period
Solutions, first period
Master's Programme in Mathematics and Statistics is responsible for the course.
Belongs to the Mathematics and Applied mathematics module.
The course is available to students from other degree programmes.
Analysis I&II, Linear algebra I&II, Topology I
Elements of measure theory and complex analysis
Elements of linear functional analysis including Banach and Hilbert spaces and linear operators between them, three basic principles, and applications to differential equations.
Recommended time/stage of studies for completion: 1. year
Term/teaching period when the course will be offered: varying
Introduction to linear functional analysis including Banach and Hilbert spaces and linear operators between them; topology of normed spaces; examples of Banach spaces including sequence and function spaces; three basic principles; Fourier-series; Sobolev spaces; applications to differential equations.
Funktionaalianalyysin peruskurssi, luentomoniste.
Rynne, B., Youngson, M., Linear Functional Analysis, Springer Undergraduate Mathematics Series, London, 2000. (Introduction to the topic)
Friedman, A., Foundations of Modern Analysis, Dover 1982. Conway, J. A Course in Functional Analysis. Springer, 1990. (Introduction to the topic) Werner, D., Funktionalanalysis, Springer Lehrbuch 1990. (In German)
Lectures and exercise classes
Exam and excercises, Course will be graded with grades 1-5.
Exam, other methods will be described later.