Each lecture will be accompanied by a problem set that revisits and expands on a selection of topics from the lecture. These exercises will be discussed in the exercise session on Mondays, according to the following two-week rhythm:
The context of each exercise, and possibly hints towards its solution, are given.
You have one week to work on solutions and hand them in.
Another week later, solutions are discussed in the exercise session.
While you are not required to hand in solutions, you are encouraged to do so. Irrespective of this, you should present (at least) one problem and its solution in an exercise session.
Note: The exercise sessions begin on Monday, February 24.
This course offers an introduction to the theory of distributions, extending classical analysis to handle functions and operators in cases where traditional techniques fail, such as at points of discontinuity or singularity.
Key topics include the definition and functional analytic aspects of distributions, test functions, and operations on distributions such as differentiation, convolution, and Fourier transforms. Special emphasis is placed on their applications in the context of partial differential equations (PDEs), via e.g. fundamental solutions and parametrices.
Literature
Some references for this course are the books
"Real Analysis"by Gerald B. Folland
"Functional Analysis" by E.M. Stein and R. Shakarchi
"Funktionalanalysis" by D. Werner
"Analysis and Partial Differential Equations" by T. Alazard
"Distributions, Partial Differential Equations, and Harmonic Analysis" by D. Mitrea
Exam
The exam will be oral, 30 minutes duration. Topics include all material from the lecture and the exercises. Active participation in the exercise session is thus highly encouraged.
