Description
Instructor(s)/Supervisor(s)/Coordinator(s): Tianling JINBanach space. Hahn-Banach theorem, open mapping theorem, closed graph theorem, uniform boundedness theorem, separation theorem, Krein-Milman theorem. Weak topologies and weak topologies, reflexive spaces, separable spaces, Arzela-Ascoli theorem, uniform convexity. Hilbert space, Riesz representation theorem and Lax-Milgram theorem. Adjoints and duality. Compact, Fredholm, self-adjoint operators and their spectrum. Sobolev spaces, Sobolev inequalities, elliptic boundary value problems, and other applications.