MATS220 Functional Analysis (10 cr)

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Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023

Description

Hilbert spaces and Banach spaces, bounded linear operators, Fourier series, Baire category, weak topology, the spectrum of an operator.

Learning outcomes

The student
  • masters the basic fundamental results of the theory of  Banach and Hilbert spaces.
  • has obtained skills to apply the theory of  Banach and Hilbert spaces in modern analysis.

Description of prerequisites

Metric spaces, Topology, Measure and integration theory 1 and 2.

Literature

  • Andrew M. Bruckner, Judith B. Bruckner & Brian S. Thomson: Real Analysis, 2008, www.classicalrealanalysis.com
  • Avner Friedman, Foundations of modern analysis, Dover Publications Inc. 1982; ISBN: 0-486-64062-0
  • John B. Conway, A course in functional analysis (2nd edition), Springer, 1990; ISBN: 0-387-97245-5
  • Lauri Kahanpää, Funktionaalianalyysi, luntomoniste 51, Matematiikan ja tilastotieteen laitos, Jyväskylän yliopisto, 2004.; ISBN: 951-39-1763-0

Completion methods

Method 1

Evaluation criteria:
Course exam and exercises
Time of teaching:
Period 3, Period 4
Select all marked parts

Method 2

Evaluation criteria:
final exam
Select all marked parts
Parts of the completion methods
x

Teaching (10 cr)

Type:
Participation in teaching
Grading scale:
0-5
Language:
English, Finnish
Study methods:

Lectures and exercises

Teaching

x

Exam (10 cr)

Type:
Exam
Grading scale:
0-5
Language:
English, Finnish

Teaching