Learning outcomes

The aim of the course is to study the important theorems of Fonctional Analysis in the framework of normed spaces of infinite dimension and to apply them to the solution of linear functional equations.

Content

Linear and bounded operators. Hahn-Banach theorems, separation of convex sets, Banach-Steinhaus theorem. Open mapping theorem and closed graph theorem. After that the weak and weak-* topologies are studied (Banach-Alaoglu theorem and reflexiive spaces). The second part of the course is devoted to the spectral theory of compact operators (Neumann lemma, Fredholm Alternative theorems. Finally the obtained results are applied for solving integral equations in the framework of Hilbert spaces.

Assessment method

An oral test to check the theory and a written test to evaluate the capacity of the students to make exercises.

Sources, references and any support material

There exists an English version of Analyse fonctionnelle. Théorie et applications Haim Brezis Masson Paris 1983 :

 

 

H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer 2011.

Language of instruction

Français
Training Study programme Block Credits Mandatory
Standard 0 6
Standard 3 6