Harmonic analysis 2
General data
Course ID: | 1000-1M10AH2 |
Erasmus code / ISCED: |
11.134
|
Course title: | Harmonic analysis 2 |
Name in Polish: | Analiza harmoniczna 2 |
Organizational unit: | Faculty of Mathematics, Informatics, and Mechanics |
Course groups: |
(in Polish) Przedmioty obieralne na studiach drugiego stopnia na kierunku bioinformatyka Elective courses for 2nd stage studies in Mathematics |
ECTS credit allocation (and other scores): |
6.00
|
Language: | English |
Type of course: | elective monographs |
Requirements: | Analytic Functions of One Complex Variable 1000-134FAN |
Prerequisites: | Harmonic analysis 1000-1M10AH |
Short description: |
The lecture 'Harmonic Analysis 2' is planned as the continuation of 'Harmonic analysis', but passing the aforementioned course is not necessary. |
Full description: |
The lecture 'Harmonic Analysis 2' is planned as the continuation of 'Harmonic analysis' . Plan: - classical properties of Fourier transform on R^{n} - distributions - Calderon-Zygmund theory - multiplier theorems - other topics depending on the students interest |
Bibliography: |
- W. Rudin Fourier Analysis on Groups - A. Zygmund Trigonometric Series - C.C. Graham, O. C. McGehee Essays in Commutative Harmonic Analysis - E. M. Stein and G. Weiss Introduction to Fourier Analysis in Euclidean Spaces - Y. Katznelson An Introduction to Harmonic Analysis - R. E. Edwards Fourier Series, a Modern Introduction - E. Hewitt and K. A. Ross Abstract Harmonic Analysis - E. M. Stein and R. Shakarchi Fourier Analysis, an Introduction - H. Helson Harmonic Analysis |
Learning outcomes: |
Student after taking the course 'harmonic analysis II': 1. Know and understand basic topics connected to Fourier transform. 2. Is able to use the knowledge on Fourier transform in applications to classical analysis. 3. Understands why harmonic analysis on the real line is very much different from harmonic analysis on the circle group. 4. Can use the language of distributions in other branches of analysis (for example partial differential equations). 5. Can point out how the smoothnes properties of a function affects the Fourier transform. 6. Can apply Calderon-Zygmund theory to operators appearing in other branches of analysis. 7. Can apply multiplier theorems to various classes of operators. |
Assessment methods and assessment criteria: |
At the end of the semester the written exam is planned. Its result combined with the level of acitivity during the exercise sessions will be the base for a preliminary mark. The student interested in increasing his grade will be asked for the oral exam. The most active students during exercise sessions will be rewarded with the maximum grade and may be exempted from the written exam. |
Classes in period "Winter semester 2023/24" (past)
Time span: | 2023-10-01 - 2024-01-28 |
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MO TU W WYK
CW
TH FR |
Type of class: |
Classes, 30 hours
Lecture, 30 hours
|
|
Coordinators: | Przemysław Ohrysko | |
Group instructors: | Przemysław Ohrysko | |
Students list: | (inaccessible to you) | |
Examination: |
Course -
Examination
Lecture - Examination |
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