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
Programme
The main theorems of Functional Analysis.Core Documentation
H. Brezis, Functional Analysis.Type of delivery of the course
Many lessons.Type of evaluation
Written and oral examination. teacher profile teaching materials
Hahn-Banach theorem, analytic and geometric form, consequences.
First and second category spaces, Baire theorem, Banach-Steinhaus theorem, open map and closed graph, applications.
Weak, closed and convex topologies, Banach-Alaoglu Theorem, separability, reflexivity and uniform convexity.
Sobolev spaces in one dimension, embedding 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);
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 theorem, Banach-Steinhaus theorem, open map and closed graph, applications.
Weak, closed and convex topologies, Banach-Alaoglu Theorem, separability, reflexivity and uniform convexity.
Sobolev spaces in one dimension, embedding 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);
Reference Bibliography
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
In person lecturesType of evaluation
the test consists in carrying out exercises and presenting topics discussed in class teacher profile teaching materials
Mutuazione: 20410637 AM450 - ANALISI FUNZIONALE in Matematica LM-40 BESSI UGO, PROCESI MICHELA
Programme
The main theorems of Functional Analysis.Core Documentation
H. Brezis, Functional Analysis.Reference Bibliography
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
Many lessons.Type of evaluation
Written and oral examination. teacher profile teaching materials
Hahn-Banach theorem, analytic and geometric form, consequences.
First and second category spaces, Baire theorem, Banach-Steinhaus theorem, open map and closed graph, applications.
Weak, closed and convex topologies, Banach-Alaoglu Theorem, separability, reflexivity and uniform convexity.
Sobolev spaces in one dimension, embedding 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);
Mutuazione: 20410637 AM450 - ANALISI FUNZIONALE in Matematica LM-40 BESSI UGO, PROCESI MICHELA
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 theorem, Banach-Steinhaus theorem, open map and closed graph, applications.
Weak, closed and convex topologies, Banach-Alaoglu Theorem, separability, reflexivity and uniform convexity.
Sobolev spaces in one dimension, embedding 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);
Reference Bibliography
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
In person lecturesType of evaluation
the test consists in carrying out exercises and presenting topics discussed in class