ECTS : 8
Volume horaire : 78
Description du contenu de l'enseignement :
Detailed schedule :
CM : 39h00
TD : 39h00
1. Compactnes in metric spaces; Riesz compactness theorem; Arzelà-Ascoli theorem.
2. Hahn-Banach theorem, Baire category theorem, uniform boundedness principle, open mapping theorem, closed graph theorem.
3. Hilbert spaces: projection on a closed convex subset, orthonormal bases, Riesz representation theorem (review of last year’s course); Lax-Milgram theorem.
4. Weak convergence in Hilbert spaces.
5. Spectrum of a bounded operator in a Banach space; the case of compact operators.
6. Self-adjoint compact operators in Hilbert spaces: the spectral theorem.
7. Sobolev spaces in one space dimension.
Compétence à acquérir :
This course presents classical results of functional analysis and some of their applications.