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28393 - Functional Analysis 1

Academic Year 2019/2020

                
                        Docente:
                        Davide Guidetti
                    
                        Credits:
                        6
                    
                        SSD:
                        MAT/05
                    
                        Language:
                        Italian
                    
                        Teaching Mode:
                        Traditional lectures
                        
                            Campus:
                            Bologna
                        
                            Corso:
                            First cycle degree programme (L) in
                            Mathematics (cod. 8010)

                            Teaching resources on Virtuale

Learning outcomes

At the end of the course, the student should have acquired the basic competences of functional analysis and of the theory of bounded and linear operators.

Course contents

Abstract theiry of measure and integration. Metric spaces. Normed spaces. Hilbert spaces. Orthonormal systems. Fourier series. Basic spectral theory. The theorems of approximation of Weierstrass and Stone. The theorems of the open mapping, Banach-Steinhaus and Hahn-Banach.

Readings/Bibliography

W. Rudin, "Real and c omplex analysis", K. Saxe, "Beginning functional analysis", H. Brezis "Functional analysis".

Teaching methods

Front lectures

Assessment methods

Oral examination

Teaching tools

Blackboard

Office hours

See the website of Davide Guidetti