Введение в функциональный анализ
- Students will be introduced to the basic notions and the basic principles of Functional Analysis.
- Prove the completeness of classical function spaces
- Calculate the norms of linear operators
- Apply the basic principles of Functional Analysis in concrete situations.
- Find the spectra of linear operators by using, in particular, duality theory
- Normed and Banach spaces, bounded linear maps.
- Hilbert spaces.
- The Hahn-Banach Theorem, the Open Mapping Theorem, the Uniform Boundedness Principle.
- Compact operators. The Hilbert-Schmidt Theorem.
- Elementary spectral theory.
- Basic duality theory.
- midterm gradeThe midterm exam (oral) will be at the end of October (or at the beginning of November) and will include only the material of the 1st module.
- exercise sheets gradeTo get the maximum grade for the exercise sheets, you should solve 75% of all the exercises. If you solve more, you will earn bonus points. You can also earn bonus points for working actively at the exercise classes and for solving «bonus exercises» (marked as «B» in the sheets).
- final examThe oral exam will be at the end of December and will include only the material of the 2nd module.
- Interim assessment (2 module)0.35 * exercise sheets grade + 0.3 * final exam + 0.35 * midterm grade
- Simon, B. (2015). Real Analysis. Providence, Rhode Island: AMS. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1347487
- Reed, M. (1972). Methods of Modern Mathematical Physics : Functional Analysis. Oxford: Academic Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=567963