Studying at the University of Verona

Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.

Study Plan

The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.

CURRICULUM TIPO:

1° Year 

ModulesCreditsTAFSSD
6
B
MAT/08
6
B
MAT/07
6
B
MAT/03
12
B
MAT/05
6
B
MAT/05
6
C
MAT/06

2° Year   activated in the A.Y. 2015/2016

ModulesCreditsTAFSSD
6
B
MAT/05
32
E
-
activated in the A.Y. 2015/2016
ModulesCreditsTAFSSD
6
B
MAT/05
32
E
-
Modules Credits TAF SSD
Between the years: 1°- 2°
three course to be chosen among the following
6
C
MAT/03
6
C
MAT/08
6
C
MAT/02
6
C
MAT/02
6
C
MAT/06
6
C
MAT/05
6
C
INF/01
6
C
MAT/09
6
C
MAT/07
6
C
MAT/08
6
C
MAT/08
Between the years: 1°- 2°
A course to be chosen among the following
6
B
MAT/02
6
B
MAT/02
Between the years: 1°- 2°
12
D
-
Between the years: 1°- 2°
Other activitites
4
F
-

Legend | Type of training activity (TTA)

TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.

A Basic activities
B Characterizing activities
C Related or complementary activities
D Activities to be chosen by the student
E Final examination
F Other training activities
S Placements in companies, public or private institutions and professional associations

Functional analysis (2014/2015)

Teaching code

4S001101

Credits

12

Coordinator

Sisto Baldo

Language

English en

Scientific Disciplinary Sector (SSD)

MAT/05 - MATHEMATICAL ANALYSIS

Seminars 0

The teaching is organized as follows:

Parte 1

Credits

6

Period

I sem.

Academic staff

Sisto Baldo

Parte 3

Credits

3

Period

I sem.

Academic staff

Marco Squassina

Parte 2

Credits

3

Period

I sem.

Academic staff

Giandomenico Orlandi

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.

Program

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.

Bibliography

Reference texts
Activity Author Title Publishing house Year ISBN Notes
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

Examination Methods

Written and oral test.

Students with disabilities or specific learning disorders (SLD), who intend to request the adaptation of the exam, must follow the instructions given HERE

Teaching materials e documents