Mathematical analysis III (MAT903)

The course is aimed at PhD students in complex and harmonic analysis and will consist of three blocks, each corresponding to 5 credit points. The first block is part of a general mathematical education and is compulsory for all the analysis PhD students, while the second part of the course is on more specific subjects and to be chosen from the second and third blocks.


Course description for study year 2024-2025

Facts

Course code

MAT903

Version

1

Credits (ECTS)

10

Semester tution start

Spring, Autumn

Number of semesters

1

Exam semester

Spring, Autumn

Language of instruction

Norwegian

Offered by

Content

Description: The course is aimed at PhD students in complex and harmonic analysis and will consist of three blocks, each corresponding to 5 credit points. The first block is part of a general mathematical education and is compulsory for all the analysis PhD students, while the second part of the course is on more specific subjects and to be chosen from the second and third blocks.

Literature: W. Rudin, Real and Complex Analysis; T. Ransford, Potential Theory in the Complex Plane; A. Olevskii and A. Ulanovskii, Functions with Disconnected Spectrum; M. Klimek, Pluripotential Theory.

Learning outcome

After finishing the course, the student will have knowledge of measure theory and integration, as well as basics of potential theory. In addition, the student will learn either main ideas of Fourier analysis, including sampling and interpolation of band-limited functions (option 1), or of basics on holomorphic functions of several variables, complex manifolds and pluripotential theory.

Module 1 (5ECTS- FIXED): Measure theory, integration and potential theory

Contents: general measure theory and Lebesgue integration; basics of potential theory in the complex plane and Rn.

Module 2 (5ECTS - option1): Fourier analysis

Contents: Fourier transform; functional spaces; sampling and interpolation of band-limited functions.

Module 3 (5ECTS - option2): Several complex variables and pluripotential theory

Contents: basics on holomorphic functions of several variables; complex manifolds; introduction to pluripotential theory.

Required prerequisite knowledge

None

Exam

Form of assessment Weight Duration Marks Aid
Oral exam 1/1 Passed / Not Passed

Course teacher(s)

Course teacher:

Tyson Ritter

Course teacher:

Alexander Ulanovskii

Course coordinator:

Alexander Rashkovskii

Method of work

Lectures, seminars, guided reading

Overlapping courses

Course Reduction (SP)
Fourier and Wavelet Analysis (MAT900_1) 5
Functional Analysis with Applications (MAT901_1) 5

Open for

Technology and Natural Science - PhD programme

Course assessment

There must be an early dialogue between the course supervisor, the student union representative and the students. The purpose is feedback from the students for changes and adjustments in the course for the current semester.In addition, a digital subject evaluation must be carried out at least every three years. Its purpose is to gather the students experiences with the course.

Literature

Search for literature in Leganto