Harmonic analysis 2

General data

Course ID:	1000-1M10AH2
Erasmus code / ISCED:	11.134 The subject classification code consists of three to five digits, where the first three represent the classification of the discipline according to the Discipline code list applicable to the Socrates/Erasmus program, the fourth (usually 0) - possible further specification of discipline information, the fifth - the degree of subject determined based on the year of study for which the subject is intended. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
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):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	English
Type of course:	elective monographs
Requirements:	Analytic Functions of One Complex Variable 1000-134FAN Functional Analysis 1000-135AF
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.

This course is not currently offered.

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