MA8106 - Harmonic Analysis

Examination arrangement

Examination arrangement: Oral examination

Evaluation Weighting Duration Grade deviation Examination aids
Oral examination 100/100 E

Course content

This course is taught every second year, next time Spring 2022, provided there is a suffient number of students attending. If there are not enough students, the course may be offered as a supervised self-study. The course will treat central concepts and results in modern harmonic analysis, which are developments from classical Fourier analysis. One possible theme may be harmonic analysis related to the study of singular integrals and complex and real methods. Some key concepts are: maximal functions, Calderon-Zygmund decompositions, the Hilbert transform, Littlewood-Paley theory, Hardy spaces, Carleson measures, Cauchy integrals, singular integral operators. The course may also cover a more abstract direction dealing with generalizations of classical Fourier analysis from the unit circle to locally compact Abelien groups. Key concepts are then Haar measure, convolution, the dual group and Fourier transformation, positive definite functions, the inversion theorem, Plancherel's theorem, Pontryagin's duality theorem, the Bohr compactification.

Learning outcome

1. Knowledge. The course will treat central concepts and results in modern harmonic analysis, which are developments from classical Fourier analysis. One possible theme may be harmonic analysis related to the study of singular integrals and complex and real methods. Some key concepts are: maximal functions, Calderon-Zygmund decompositions, the Hilbert transform, Littlewood-Paley theory, Hardy spaces, Carleson measures, Cauchy integrals, singular integral operators. The course may also cover a more abstract direction dealing with generalizations of classical Fourier analysis from the unit circle to locally compact Abelien groups. Key concepts are then Haar measure, convolution, the dual group and Fourier transformation, positive definite functions, the inversion theorem, Plancherel's theorem, Pontryagin's duality theorem, the Bohr compactification. 2. Skills. The students should learn the basics of the contemporary Harmonic Analysis and be able to apply its methods in related subjects of Mathematics. 3. Competence. The students should be able to participate in scientific discussions and conduct researches on high international level in contemporary and classical Harmonic analysis as well as its applications to various areas of Mathematics.

Learning methods and activities

Lectures, alternatively supervised self-study.

Course materials

Will be announced at the start of the course.

More on the course
Facts

Version: 1
Credits:  7.5 SP
Study level: Doctoral degree level

Coursework

Term no.: 1
Teaching semester:  SPRING 2022

Language of instruction: -

Location: Trondheim

Subject area(s)
• Mathematics
Contact information
Course coordinator:

Department of Mathematical Sciences

Examination

Examination arrangement: Oral examination

Term Status code Evaluation Weighting Examination aids Date Time Examination system
Autumn ORD Oral examination 100/100
Spring ORD Oral examination 100/100
• * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
Examination

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