Details
Overview
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
- "Analysis and Partial Differential Equations" by T. Alazard
- "Real Analysis" by Gerald B. Folland
- "Distributions, Partial Differential Equations, and Harmonic Analysis" by D. Mitrea
- "Functional Analysis" by E.M. Stein and R. Shakarchi
- "Funktionalanalysis" by D. Werner
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.
Für weitere Informationen kontaktieren Sie bitte: Prof. Dr. Klaus Widmayer