Functional analysis (2015/2016)

Course code
4S001101
Credits
12
Coordinator
Sisto Baldo
Academic sector
MAT/05 - MATHEMATICAL ANALYSIS
Language of instruction
English
Teaching is organised as follows:
Activity Credits Period Academic staff Timetable
Parte 1 6 I semestre Sisto Baldo
Parte 2 3 I semestre Giandomenico Orlandi
Parte 3 3 I semestre Marco Squassina

Lesson timetable

I semestre
Activity Day Time Type Place Note
Parte 1 Monday 11:30 AM - 1:30 PM lesson Lecture Hall M  
Parte 1 Tuesday 12:30 PM - 2:30 PM lesson Lecture Hall I  
Parte 1 Wednesday 8:30 AM - 9:30 AM lesson Lecture Hall M  
Parte 1 Wednesday 9:30 AM - 10:30 AM lesson Lecture Hall M  
Parte 1 Thursday 10:30 AM - 12:30 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 test.

Teaching aids
Title Format (Language, Size, Publication date)
Lecture Notes (Sisto Baldo)  pdfpdf (en, 696 KB, 25/11/15)
course diary - 2nd part  pdfpdf (it, 301 KB, 26/01/16)

STUDENT MODULE EVALUATION - 2015/2016