Mathematical Analysis 5

The course aims at presenting some fundamental topics of Functional Analysis. The first part will be focused on the study of Lebesgue spaces, namely spaces of p-summable functions. The second part will be devoted to the development of the theory of Hilbert spaces and of the operators defined on them.

Students will become acquainted with some fundamental concepts of Functional Analysis. Upon completion of the course, they will have acquired the knowledge needed to take advanced courses in several areas of study, such as Mathematical Analysis, Probability, Geometry, Mathematical Physics, Mathematical Finance, and Numerical Analysis.
By the end of the classes, the students will have learnt several key results, will be able to provide rigorous proofs of them, and will have developed the ability to autonomously produce abstract arguments to justify more elementary statements. To complement this theoretical training, they will also become capable of solving problems involving concrete reasoning and explicit computations.