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Università degli Studi di Parma Università degli Studi di Parma
Degree course in
Mathematics
Università degli Studi di Parma
Department of Mathematical, Physical and Computer Sciences

FUNCTION SPACE
cod. 14842

Academic year 2012/13
3° year of course - First semester
Professor
Academic discipline
Analisi matematica (MAT/05)
Field
Formazione teorica
Type of training activity
Characterising
48 hours
of face-to-face activities
6 credits
hub:
course unit
in - - -
lectures timetable unavailable
exam calls
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Learning objectives

The course it is aimed at illustrating the main results from Functional analysis and from the Lp theory.

Prerequisites

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Course unit content

1) Topological vector spaces, locally convex spaces.
2) Linear operators in topological vector spaces
3) Normed spaces and Banach spaces
4) Operators on normed spaces
5) Hahn-Banach theorem and its consequences.
6) Banach-Steinhaus theorem and its consequences
7) Open mapping theorem and its consequences
8) Weak topologies in Banach spaces
9) Reflexive spaces
10) Hilbert spaces: main properties
11) Projections in Hilbert spaces and their applications
12) Orthonormal systems
13) Fourier series in Hilbert spaces
14) Convolutions
15) Lp spaces.

Full programme

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Bibliography

1) Lecure notes by the teacher

2) H. Brezis. Functional analysis, Sobolev spaces and partiare differential equations, Springer Verlag 2011.

3) W. Rudin, Functional analysis, McGraw-Hill,
New York 1973.

Teaching methods

Lectures. During the lectures the basic results of the functional analysis will be analyzed and discussed. Many examples will be provided to show how and where the
abstract results can be applied to make the students understand better the relevance of what they are studying.

Assessment methods and criteria

The exam consists of two parts: a written part and an oral part. The exam is aimed at evaluating the knowledge of the abstract results seen during the course, their proofs and the skills of the students in using such results.

Other information

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