Selected Topics in Analysis and Applications

Modern concepts of Analysis, including Distributions, Sobolev spaces, Fourier analysis, Inequalities, Banach and Hilbert spaces, spectral theorem, etc. The various concepts will be illustrated with examples of applications in physics. Sample literature:

• Lieb-Loss: Analysis. Amer. Math. Soc. 2001.
• Rudin: Real and Complex Analysis. McGraw-Hill 1987.
• Reed-Simon: Functional Analysis. Academic Press 1980.

Target group: First year PhD students in Mathematics.

Prerequisites: Calculus and undergraduate real analysis (in the US system); equivalently Analysis I—III (German system) and linear algebra.

Evaluation: Homework assignments and exam (take home)

Teaching format: Lectures + recitation

ECTS: 6 Year: 2024

Track segment(s):
Elective

Teacher(s):
Julian Fischer Robert Seiringer

Teaching assistant(s):
Lorenzo Pigozzi