To acquire a good knowledge of functional analysis: Banach and Hilbert spaces, weak topologies, linear and continuous operators, compact operators, spectral theory.
Curriculum
teacher profile teaching materials
W. Rudin, Functional Analysis.
Fruizione: 20410637 AM450 - ANALISI FUNZIONALE in Matematica LM-40 BESSI UGO
Programme
The Hahn-Banach theorem; the open mapping theorem, the closed graph theorem and the Banach-Steinhaus theorem. Weak topologies, Banach-Alaoglu theorem and reflexivity. Linear continuous operators and the spectral theorem for compact, self-adjoint operators. Sobolev spaces and elliptic problems in one dimension. The spectral theorem for unitary operators.Core Documentation
H. Brezis, Analisi funzionale.W. Rudin, Functional Analysis.
Type of evaluation
Written and oral examinations; it is possible to skip the written examination at the end if the student passes two written mini-tests during the course. teacher profile teaching materials
W. Rudin, Functional Analysis.
Fruizione: 20410637 AM450 - ANALISI FUNZIONALE in Matematica LM-40 BESSI UGO
Programme
The Hahn-Banach theorem; the open mapping theorem, the closed graph theorem and the Banach-Steinhaus theorem. Weak topologies, Banach-Alaoglu theorem and reflexivity. Linear continuous operators and the spectral theorem for compact, self-adjoint operators. Sobolev spaces and elliptic problems in one dimension. The spectral theorem for unitary operators.Core Documentation
H. Brezis, Analisi funzionale.W. Rudin, Functional Analysis.
Type of evaluation
Written and oral examinations; it is possible to skip the written examination at the end if the student passes two written mini-tests during the course.