| Crédit : 10 ECTS |
| Langue du cours : anglais
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Volume horaire
- CM :
78 h
- Volume horaire global (hors stage) :
78 h
Compétences à acquérir
Classical results in functional analysis and some of their applications.
Description du contenu de l'enseignement
The course presents functional analysis methods for solving partial differential equations.
- Compactness in metric spaces; Riesz compactness theorem; Arzelà-Ascoli theorem.
- Hahn-Banach theorem, Baire category theorem, theorem of Banach-Steinhaus, open mapping theorem, closed graph theorem.
- Hilbert spaces: projection, Hilbert bases, Riesz isomorphism theorem (reminders), Lax-Milgram theorem, weak convergence
- Spectral theory: spectrum of bounded operators in Banach spaces, compact and self-adjoint operators in Hilbert spaces, spectral theorem
- Sobolev spaces in one space dimension.
Enseignant responsable
ERIC SERE