MAT4400 – Linear Analysis with Applications

Schedule, syllabus and examination date

Course content

The course gives a thorough introduction to measure and integration theory together with a basic introduction to functional analysis. Covered topics include Banach and Hilbert spaces, Hahn-Banach theorem, dual spaces, orthonormal bases, measure spaces, Lebesgue integration, convergence theorems, Lp-spaces and their duals, construction and decomposition of measures, Lebesgue and Lebesgue-Stieltjes measures, Littlewood’s principles, Riesz-Markov theorem, product measures and Fubini-Tonelli theorems, fundamental theorem of calculus, Fourier transform and Plancherel theorem, conditional expectations and martingales.

Learning outcome

After completing the course you

  • are used to work with measure spaces and integration of measurable functions

  • have a good understanding of the most frequently used tools of Lebesgue integration such as convergence theorems and Fubini-Tonelli theorems

  • have a good understanding of various function spaces and their duals

  • are acquainted with basic notions of functional analysis

  • are familiar with fundamental tools of Fourier analysis

  • are prepared for more advanced courses on differential equations, harmonic, stochastic and functional analysis

Admission to the course

Students admitted at UiO must?apply for courses?in Studentweb. Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme.

Nordic citizens and applicants residing in the Nordic countries may?apply to take this course as a single course student.

If you are not already enrolled as a student at UiO, please see our information about?admission requirements and procedures for international applicants.

Overlapping courses

Teaching

6 hours of lectures/exercises every week throughout the semester.

The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.

Examination

Final written exam which counts 100 % towards the final grade.?

This course has 1 mandatory assignment that must be approved before you can sit the final exam. The assignment must be written with a typesetting software for mathematics, e.g. LaTeX.

It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses: MAT3400 – Linear Analysis with Applications