MAT3400 – Linear Analysis with Applications
Course description
Course content
The course provides advanced knowledge in measure and integration theory together with a basic introduction to functional analysis. Covered topics include Banach and Hilbert spaces, the Hahn-Banach theorem, dual spaces, orthonormal bases, Jacobi’s transformation theorem, Lp-spaces and their duals, construction and decomposition of measures, Lebesgue-Stieltjes measures, the Riesz-Markov theorem, product measures and the Fubini-Tonelli theorems, the Radon-Nikodym theorem, the fundamental theorem of calculus, the Fourier transform and the Plancherel theorem, characteristic functions and conditional expectations.
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 the