Mathematics

FILOMENA PACELLA

Educational Goals

General objectives: To provide students with the basics related to the study of functional spaces that intervene in various fields. In particular, linear operators will be studied between Banach or Hilbert spaces and their spectrum will be analyzed. Finally, some non-linear Functional Analysis techniques will be presented, suitable for the study of differential problems.

Specific objectives:

Knowledge and understanding: at the end of the course the student will have acquired the basic notions and results related to the Functional Analysis and to its different applications to differential problems.

The students will learn the basic theory of Banach and Hilbert spaces as wellas its applications to function spaces. Moreover will be able to analyze linear operators and understand their spectrum.

Differential and Integral Calculus for functions of several variables. Basic notions of Real Analysis and of Topology.

Normed space and bounded linear operators. Hahn-Banach theorems and applications. Baire's theorem and applications. Weak topologies. Reflexive spaces. Hilbert spaces. Compact operators and their spectrum.

S.Kesavan Functional Analysis ed. Hindustan Book Agency
H.Brezis Analisi Funzionale ed. Liguori
S.Kesavan Topics in Functional Analysis and Applications ed. New Age Internatioonal
(Wiley-Eastern) (only for the eigenvalues of the Laplace operator))

The classes will be given on a blackboard

It is advisable to attend all the classes

The evaluation is based on a written exam about simple exercises as application of the theory and on an oral exam about theorems and their proofs.

Statements and proofs of the main theorems. Applications shown during the course.