Basics of measure and integration theory
This course introduces the participants to some of the fundamental parts of functional analysis, a discipline that is concerned with ubiquitous abstract structures in analysis. It covers the basic theory of Hilbert and Banach spaces and their operators.
Knowledge of the concepts of normed space, Banach space, Hilbert space, orthonormal basis, linear operator, bounded operator, dual space.
Knowledge of the theorems of Hahn-Banach, Banach-Steinhaus, closed graph, and bounded inverse.
The ability to apply these concepts and theorems to solve problems in functional analysis.
Mode of instruction
Lecture (2 hours) and question hour (non-compulsory).
Written exam and homework. During the course, there will be six homework assignments to be handed in at predetermined dates. Out of these, the five best count towards the final grade. For the final grade, the homework counts for 25% and the written exam for 75%, unless the grade for the written exam is higher than the aforementioned weighted average. In the latter case, the final grade is equal to the the grade for the written exam.
Compulsory: “Linear Functional Analysis” by Rynne and Youngson, 2nd ed., Springer, 2008, ISBN: 978-1-84800-004-9.
For students, a paper version of this book is also available for approximately 25 euro via the MyCopy-option in SpringerLink.
Alternatively, a free PDF can legally be obtained by students via SpringerLink.
Please note that one has to use a computer at the Mathematical Institute for both these options.
Enrollment in Brightspace is compulsory.