Harmonic Analysis (MAE718)

Undergraduate Courses Outlines - Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	MAE718
Semester	7
Course Title	Harmonic Analysis
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 3, Credits: 6)
Course Type	Special Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes (In English)
Course Website (URL)	-

Learning Outcomes

Learning outcomes	The aim of the course is the achievement by the undergraduate student of the theoretical background in the theory of Fourier series
General Competences	The objective of the course is the undergraduate student's ability achievement in analysis and synthesis of the basic background in Harmonic Analysis.

Syllabus

Trigonometric polynomials, partial sums of the Fourier series of a function and -estimates, Bessel's inequality, Lemma Riemann-Lebesgue, Parseval's identity for Riemann integrable functions on , complex Riemann integrable functions defined on an interval, Fourier coefficients and Fourier series, the Dirichlet kernel, criteria for uniform convergence of the Fourier series, convolution of functions and approximations to the identity, Fejer kernel, theorem of Fejer, Poisson kernel, Abel summability of the Fourier series, applications.

Teaching and Learning Methods - Evaluation

Delivery	Face-to-face
Use of Information and Communications Technology	-
Teaching Methods	Activity Semester Workload Lectures 39 Independent study 78 Exercises solutions 33 Course total 150
Student Performance Evaluation	Written examination at the end of the semester.

Attached Bibliography

• Yitzhak Katznelson, An Introduction to Harmonic Analysis, Dover Edition.
• Elias M. Stein, Rami Shakarchi, Fourier Analysis, An Introduction, Princeton University Press.