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Harmonic Analysis (MAE718): Διαφορά μεταξύ των αναθεωρήσεων

Harmonic Analysis (MAE718): Διαφορά μεταξύ των αναθεωρήσεων

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[[Undergraduate Courses Outlines]] - [https://math.uoi.gr  Department of Mathematics]
* [[Αρμονική Ανάλυση (MAE718)|Ελληνική Έκδοση]]
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=== General ===
=== General ===
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=== Syllabus ===
=== 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.
Trigonometric polynomials, partial sums of the Fourier series of a function, Bessel's inequality, Lemma Riemann-Lebesgue, Parseval's identity for Riemann integrable functions, 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 ===
=== Teaching and Learning Methods - Evaluation ===
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=== Attached Bibliography ===
=== Attached Bibliography ===
* Yitzhak Katznelson, An Introduction to Harmonic Analysis, Dover Edition.
 
* Elias M. Stein, Rami Shakarchi, Fourier Analysis, An Introduction, Princeton University Press.
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See the official [https://service.eudoxus.gr/public/departments#20 Eudoxus site] or the [https://cloud.math.uoi.gr/index.php/s/62t8WPCwEXJK7oL local repository] of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
 
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Τελευταία αναθεώρηση της 12:31, 15 Ιουνίου 2023

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) See eCourse, the Learning Management System maintained by the University of Ioannina.

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, Bessel's inequality, Lemma Riemann-Lebesgue, Parseval's identity for Riemann integrable functions, 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

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

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