Linear Analysis treats the fundamentals of functional analysis, a discipline which is concerned with ubiquitous fundamental abstract structures in analysis. Understanding the language of functional analysis is, in fact, indispensable for various parts of both analysis and stochastics. The course covers first the basic theory of Hilbert and Banach spaces and their operators, thus providing the functional analytic vocabulary which is also necessary for other disciplines. Then it deals with the spectral theory of compact operators on Hilbert spaces. It also contains the prerequisites (!) for the national master course Functional Analysis, intended for students who want to continue in this direction in the following year.
*Remark *
It is strongly recommended that students with an interest in analysis or stochastics follow Linear Analysis in their third year, as well as Measure Theory. For other students these courses may also be a valuable addition in later years.
Lecture hours per week
2
Exam
Handing in assignments. *Literature *
Compulsory: “Linear Functional Analysis” by Rynne and Youngson, 2nd ed., Springer, 2008, ISBN: 978-1-84800-004-9. *Homepage *
Blackboard. Enrollment is compulsory.
Prerequisites
Rather limited. Basic knowledge of linear algebra (hardly beyond the notion of abstract vector spaces and linear maps) and elementary topology (metric spaces) are required.
Possible sequels
Graduation in analysis or stochastics, national courses on functional analysis, PDE or stochastics.