Mathematics: Harmonic Analysis

Harmonic analysis is a branch of mathematics concerned with representing functions or signals as the superposition of basic functions, such as wavelets. It can be seen as a generalization of Fourier series and Fourier transforms. Harmonic analysis builds on methods from functional analysis, probability, and group theory.You will learn how to apply these methods to a wide range of problems, both within mathematics and in fields like physics and data science. 

Topics include

• The maximal function
• The space BMO (functions of bounded mean oscillation) and the Carleson embedding theorem
• Muckenhoupt weights
• Fundamental operators of harmonic analysis such as singular integral operators (in particular the Hilbert transform) and the square function
• Modern discretization techniques such as wavelets (especially the Haar wavelet) and sparse domination
• Applications in other areas of mathematics, such as PDEs, and outside mathematics.

The course is alternative-compulsory within the Master’s programme in Mathematics at Lund University, and is also offered as a standalone course.

Teaching consists of lectures and seminars. Seminars focus on problem-solving and presenting relevant results. The course includes compulsory written assignments and a project. The project is presented through a written report and orally at a seminar. Peer feedback is an important part of the learning process—you will review and comment on other students’ work. Expect opportunities to develop your analytical skills and communicate complex ideas clearly. The course encourages independent thinking and creative problem-solving.

Harmonic analysis is a key tool in many advanced areas of mathematics, physics and data science. After completing the course, you will be well-prepared for further studies in aanalysis, PDEs or aapplied mmathematics. The skills you gain are also valuable in research, algorithm development, and industries working with signal processing, imaging or machine learning.

You will learn to approach complex problems with clarity and precision — a mindset that opens doors to both academic and professional paths.

Entry requirements

At least 90 credits in mathematics, including courses corresponding to MATB34 Linear Analysis, 7.5 ECTS and MATM19 Integration Theory, 7.5 ECTS , and English course 6/B.

Selection criteria

Seats are allocated according to: ECTS (HPAV): 100 %.

Tuition fees for non-EU/EEA citizens

Citizens of countries outside:

• The European Union (EU)
• The European Economic Area (EEA) and
• Switzerland

are required to pay tuition fees. You pay an instalment of the tuition fee in advance of each
semester.

Tuition fees, payments and exemptions

Full programme/course tuition fee: SEK 23,125
First payment: SEK 23,125

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Note that you may also need to pay an application fee, or provide proof of exemption.

Application fee

No tuition fees for citizens of the EU, EEA and Switzerland

There are no tuition fees for citizens of the European Union (EU), the European Economic Area (EEA) and Switzerland.