MTL874 Analysis

3 Credits (3-0-0)

Review of Banach and Hilbert spaces. The Hahn-Banach, Open mapping and Banach-Steinhaus theorems. The Riesz representation theorem, the spaces Lp(0,1) and L2(0,1) Spectral theory and SturmLiouville systems, fixed point theory. The theorems by Banach, Browder and Schauder and applications. Picard’s theorem. Integral equation of Fredholm, Volterra and Hammerstein. Nonlinear operators : The complementarity problem and its uses. Banach algebras and C* algebras. Best approximation in normed linear spaces.