Ects : 10

Enseignant responsable :

• ERIC SERE

Volume horaire : 78

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.

Compétence à acquérir :

Classical results in functional analysis and some of their applications.