Ordu University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
FMA711	INTRODUCTION TO HARMONIC ANALYSS	Compulsory	1	1	6

Level of Course Unit

Third Cycle

Objectives of the Course

in this cource, it is given an approach to basic problems of harmonic analysis by the theory of linear representations of groups

Name of Lecturer(s)

Doç. Dr. Erhan SET

Learning Outcomes

1	understand fundamental concepts of the harmonic analysis by using the theory of linear representations of groups.
2	obtain some information on solutions of main problems of the harmonic analysis by methods of the theory of linear representations of groups
3	understand applications of the harmonic analysis in different areas of mathematics and physics

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

Fourier series in Banach spaces, Fejer's theorem, convergence of Fourier series and approximation properties, some application to the theory of integral and differential equations

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	The group T of all rotations of the circle
2	Continuous linear representations of T in Banach spaces
3	Fourier series in Banach spaces
4	The Fejer’s theorem
5	The Abel-Poisson’s theorem
6	The spektrum of a point
7	Formal Fourier series
8	Midterm Exam
9	Convergences of Fourier series
10	Continuous actions of T in Banach algebras
11	Conditions of the kompactness in linear representations of T
12	Fourier series in Hilbert spaces
13	Applications to the theory of integral
14	Applications to differential equations
15	The spektrum of a linear representation
16	Final Exam

Recommended or Required Reading

Hoffman, K., Banach Spaces of Analytic Functions, Prentice-Hall iNC., Eglewood Cliffs, N., J., 1962. Katznelson, Y., An introduction to Harmonic Analysis, Dover Publ., iNC., New York, 976. Edwards, R. E., Fourier Series. A Modern introduction., Vol. i, ii., Springer, Berlin, 1979, i; 1982, ii.

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
SUM		0
End Of Term (or Year) Learning Activities	Quantity	Weight
SUM		0
Yarıyıl (Yıl) İçi Etkinlikleri		40
Yarıyıl (Yıl) Sonu Etkinlikleri		60
SUM		100

Language of Instruction

Turkish

Work Placement(s)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	2	2
Final Examination	1	2	2
Attending Lectures	3	20	60
Self Study	14	13	182
Individual Study for Mid term Examination	2	13	26
Individual Study for Final Examination	2	14	28
TOTAL WORKLOAD (hours)			300

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7
LO1
LO2
LO3

* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High