Functional analysis (2014/2015)

Course code
4S001101
Credits
12
Coordinator
Sisto Baldo
Academic sector
MAT/05 - MATHEMATICAL ANALYSIS
Language of instruction
English
Web page
http://profs.sci.univr.it/~baldo/AAcorrente/corsi.html
Teaching is organised as follows:
Activity Credits Period Academic staff Timetable
Parte 1 6 I sem. Sisto Baldo
Parte 2 3 I sem. Giandomenico Orlandi
Parte 3 3 I sem. Marco Squassina

Lesson timetable

I sem.
Activity Day Time Type Place Note
Parte 1 Monday 11:30 AM - 1:30 PM lesson Lecture Hall M  
Parte 1 Tuesday 9:30 AM - 11:30 AM lesson Lecture Hall M  
Parte 1 Wednesday 9:30 AM - 11:30 AM lesson Lecture Hall M  
Parte 1 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 test.

Reference books
Activity Author Title Publisher Year ISBN Note
Parte 1 Brezis, Haïm Analisi funzionale. Teoria e applicazioni Liguori 1986 8820715015
Parte 1 A.N. Kolmogorov, S.V. Fomin Elementi di teoria delle funzioni e di analisi funzionale (Edizione 4) MIR 1980 xxxx
Parte 1 Kolmogorov, A.; Fomin, S. Elements of the Theory of Functions and Functional Analysis Dover Publications 1999 0486406830
Parte 1 Haim Brezis Functional Analysis, Sobolev Spaces and Partial Differential Equations Springer 2011 0387709134
Teaching aids
Title Format (Language, Size, Publication date)
End term test of the Academic Year 2012-2013  pdfpdf (it, 588 KB, 28/01/15)
End term test of the Academic Year 2013-2014  pdfpdf (it, 623 KB, 28/01/15)
Lecture Notes first part (26/11/2014)  pdfpdf (it, 672 KB, 26/11/14)
Mid term test of the Academic Year 2012-2013  pdfpdf (it, 602 KB, 17/11/14)
Mid term test of the Academic Year 2013-2014  pdfpdf (it, 604 KB, 17/11/14)
Second part course notes  pdfpdf (it, 293 KB, 02/02/15)