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.
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.
Oral course for theory and exercises to illustrate it.
An oral test to check the theory and a written test to evaluate the capacity of the students to make exercises.
Functional analysis. Theo Bühler and Dietmar A. Salamon. American Mathematical Society 2018.
Functional Analysis, Sobolev Spaces and Partial Differential Equations, Haim Brezis, Springer 2011.
| Training | Study programme | Block | Credits | Mandatory |
|---|---|---|---|---|
| Bachelor in Mathematics | Standard | 0 | 5 | |
| Bachelor in Mathematics | Standard | 3 | 5 |