To acquire a good knowledge of functional analysis: Banach and Hilbert spaces, weak topologies, linear and continuous operators, compact operators, spectral theory.
teacher profile teaching materials
Hahn-Banach theorem, analytic and geometric form, consequences.
First and second category spaces, Baire's Theorem, Banach-Steinhaus Theorem, open map and closed graph theorem, applications.
Weak topologies, closed and convex sets, Banach-Alaoglu theorem, separability and reflexivity.
Sobolev spaces in dimensione one, immersion theorems, Poincaré inequality, application to variational problems.
Spectral theory, Fredholm alternative, spectral theorem for compact and self-adjoint operators, application to variational problems.
H. Brezis - Functional Analysis, Sobolev Spaces and Partial Differential Equations - Springer (2010)
W. Rudin - Functional Analysis - McGraw-Hill (1991)
Fruizione: 20410460 AM450 - ANALISI FUNZIONALE in Matematica LM-40 BATTAGLIA LUCA
Programme
Banach and Hilbert spaces, general properties, projections in Hilbert spaces, orthonormal systems.Hahn-Banach theorem, analytic and geometric form, consequences.
First and second category spaces, Baire's Theorem, Banach-Steinhaus Theorem, open map and closed graph theorem, applications.
Weak topologies, closed and convex sets, Banach-Alaoglu theorem, separability and reflexivity.
Sobolev spaces in dimensione one, immersion theorems, Poincaré inequality, application to variational problems.
Spectral theory, Fredholm alternative, spectral theorem for compact and self-adjoint operators, application to variational problems.
Core Documentation
H. Brezis - Analisi Funzionale - Liguori (1986)H. Brezis - Functional Analysis, Sobolev Spaces and Partial Differential Equations - Springer (2010)
W. Rudin - Functional Analysis - McGraw-Hill (1991)
Type of delivery of the course
Lectures.Type of evaluation
The written test can be replaced by two intermediate tests.