Lecture Notes on Functional Analysis

1. Lebesgue Measure                                            

2. Measures                                                                                                                                    

3. Measurable functions                                                                                                             

4. The Integral                                                                                                                             

5. Product Measures                                                                                                                 

6. Differentiation                                                                                                                        

7. Banach Spaces                                                                                                                      

8. Hilbert Spaces                                                                                                                     

9. L^p Spaces                                                                                                                               

10.  Linear Operators                                                                                                                 

11. Spectral Theory                                                                                                                 

Biography

Paolo Acquistapace is an associate professor of Mathematical Analysis at the University of Pisa. For more than forty years he has worked on differential equations, functional analysis and applied problems. He taught several different courses for computer science, biology, geology, mathematics, physics, engineering students, developing a large educational experience.

He taught the course of “Istituzioni di analisi matematica” for several years, researching the most effective pedagogical approach to functional analysis. Retired since 2021, Paolo Acquistapace continues his studies in functional analysis, mainly focusing on its applications to abstract control theory.