Harmonic analysis 2 1000-1M10AH2
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
Type of course
Requirements
Prerequisites
Course coordinators
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 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.
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
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: