Functional analysis (2012/2013)

Course code
4S001101
Credits
12
Coordinator
Sisto Baldo
Academic sector
MAT/05 - MATHEMATICAL ANALYSIS
Language of instruction
Italian
Web page
http://profs.sci.univr.it/~baldo/AAcorrente/corsi.html
Teaching is organised as follows:
Activity Credits Period Academic staff Timetable
Teoria 9 I semestre Sisto Baldo, Giandomenico Orlandi
Esercitazioni 3 I semestre Marco Squassina

Lesson timetable

I semestre
Activity Day Time Type Place Note
Teoria Monday 11:30 AM - 1:30 PM lesson Lecture Hall M  
Teoria Tuesday 9:30 AM - 11:30 AM lesson Lecture Hall M  
Teoria Wednesday 9:30 AM - 11:30 AM lesson Lecture Hall M  
Teoria Thursday 11:30 AM - 1:30 PM lesson Lecture Hall M  

Learning outcomes

The course introduces to the basic concepts of measure theory (Lebesgue and abstract) and of modern functional analysis, with particular emphasis on Banach and Hilbert spaces. Whenever possible, abstract results will be presented together with applications to concrete function spaces and problems: the aim is to show how these techniques are useful in the different fields of pure and applied mathematics.

Syllabus

Lebesgue measure and integral. Outer measures, abstract integration, integral convergence theorems. Banach spaces and their duals. Theorems of Hahn-Banach, of the closed graph, of the open mapping, of Banach-Steinhaus. Reflexive spaces. Spaces of sequences. Lp and W1,p spaces: functional properties and density/compactness results. Hilbert spaces, Hilbert bases, abstract Fourier series. Weak convergence and weak compactness. Spectral theory for self adjoint, compact operators. Basic notions from the theory of distributions.

Assessment methods and criteria

Written and oral exam.

Teaching aids
Title Format (Language, Size, Publication date)
Notes Prof. Orlandi  pdfpdf (en, 135 KB, 24/01/13)
Alcuni esercizi di Analisi Funzionale - Foglio 1  pdfpdf (it, 26 KB, 18/10/12)
Alcuni esercizi di Analisi Funzionale - Foglio 2  pdfpdf (it, 28 KB, 18/10/12)
Alcuni esercizi di Analisi Funzionale - Foglio 3  pdfpdf (it, 28 KB, 24/10/12)
Alcuni esercizi di Analisi Funzionale - Foglio 4  pdfpdf (it, 35 KB, 06/11/12)
Alcuni esercizi di Analisi Funzionale - Foglio 5  pdfpdf (it, 34 KB, 14/11/12)
Alcuni esercizi di Analisi Funzionale - Foglio 6  pdfpdf (it, 153 KB, 10/12/12)
Alcuni esercizi di Analisi Funzionale - Foglio 7  pdfpdf (it, 147 KB, 10/12/12)