Course Details for A.Y. 2015/2016

The information on this page refer to the academic year 2015/2016. Therefore, several links are not available and data may be incomplete. To read the current information on the course, if it is still available, go to the university course catalogue . To read information relating other academic years, use the list at the bottom of this page.

A. Year:

2015/2016

Name:

Analisi Funzionale (Istituzioni di Analisi Superiore mod.1) / Functional analysis

Type:

Module

Main course:

Istituzioni Di Analisi Superiore / Istituzioni Di Analisi Superiore

Basic information

Code:

DT0026

Sector:

MAT/05

Credits:

: Bachelor Degree in Mathematics 6 CFU (b)

Term:

1^st semester

Degree(s):

Bachelor Degree in Mathematics 3^rd anno curriculum Generale Compulsory

Language:

English

Teacher(s):

Marco Di Francesco

Propaedeutics:

Geometria III

Course Objectives

Learn the fundamental structures of Functional Analysis. Get familiar with the main examples of functional spaces, in particular with the theory of Hilbert spaces and Lebesgue spaces. Get familiar with the basic notions of operator theory. Be able to frame a functional equation in an abstract functional setting.

Course Content

Lebesgue Measure and Integration
L^p Spaces
Basic of Topological Vector Spaces, Normed and Banach Spaces, Linear Operators and linear functionals.
Hilbert Spaces
Weak topology, Weak * topology, weak compactness
Applications of Baire Category in Functional Analysis: Uniform Boundedness, Open Mapping, Closed Graph, Inverse Mapping.
Banach and Hilbert adjointness, self-adjointness
Compact Operators
Riesz Fredholm spectral theory

Learning Outcomes (Dublin Descriptors)

On successful completion of this course, the student should

Understand the theory
Be able to solve problems
Help to choose appropriate graduate studies
Practice mathematical reasoning, organize topics in logical order, connect theory to applications, elaborate independent proofs. Improve unconventional thinking.
Get the math language to study more advanced textbooks and attend research oriented courses

Prerequisites and Learning Activities

Mathematical Analysis (not only Calculus) in one and several space variable, Linear Algebra (including abstract Vector Speces), Set Topology (including Compact Spaces) and Metric Spaces, Ordinary differential equations.

Assessment Methods and Criteria

Written test.

Textbooks

Terence Tao, An introduction to measure theory. , American Mathematical Society, Providence, RI, ISBN: 978-0-8218-6919-2 . 2011.
Haim Brezis, Functional analysis, Sobolev spaces and partial differential equations. , Universitext. Springer, New York,. 2011. xiv+599 pp. ISBN: 978-0-387-70913-0
Alberto Bressan, Lecture notes on functional analysis. With applications to linear partial different , Graduate Studies in Mathematics, 143. American Mathematical Society, Providence, RI,. 2013. xii+250 pp. ISBN: 978-0-8218-8771-4
Lecture notes provided by the teacher
Michael Reed, Barry Simon, Methods of modern mathematical physics. I. Functional analysis. Second edition. , Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York,. 1980. xv+400 pp. ISBN: 0-12-585050-6
Stein, Elias M.; Shakarchi, Rami , Real analysis. Measure theory, integration, and Hilbert spaces. Princeton Lectures in Analysis, III. , Princeton University Press, Princeton, NJ,. 2005. xx+402 pp. ISBN: 0-691-11386-6

Internet Resources

Homepage:

http://univaq.it/~difrance/teaching.htm

Course page updates

This course page is available (with possible updates) also for the following academic years:

To read the current information on this course, if it is still available, go to the university course catalogue .

Course information last updated on: 03 luglio 2015, 14:59