Analysis IV ( Fourier Theory & Hilbert Spaces ), D-MATH
Spring Semester 2025
Lecturer: Prof. Francesca Da Lio
Exercise hours coordinator: Thomas Stucker
Diary of the lectures
| #Week | Date | Content | Notes | Reference |
|---|---|---|---|---|
| 1 | 20/21.02.2025 | Slides of presentation of the course Motivation to the study of Hilbert Spaces. Definition of Inner Product Spaces. Examples. Norms. Cauchy-Schwarz inequality (proof). Parallelogram law. Continuity of the inner product with respect to the product topology. | Class Notes | |
| 2 | 27/28.02.2025 |
Recommended bibliography (Undergraduate-Master level):
[Iac] Lecture Notes, Mikaela Iacobelli.
[Bo] Méthodes mathématiques pour les sciences physiques, Jena-Michel Bony École polytechnique, 2000.
[Bre] Functional Analysis, Sobolev Spaces and Partial Differential Equations Haim Brezis, (Universitext) 2011th Edition.
[Ev] Partial Differential Equations" by Evans (American Mathematical Society, Laurence Craig Evans, AMS 2010 (2nd edition).
[Y] An Introduction to Hilbert Spaces, Nicholas Young, Cambridge, Mathematical Textbooks, 1992.
Further reading:
- Terence Tao, Ask yourself dumb questions – and answer them!;
- Paul R. Halmos, How to write Mathematics
- Cédric Villani: What's so sexy about math?, https://www.youtube.com/watch?v=Kc0Kthyo0hU .