Short Course Description
Hours per week: 3
Weight: 3 credit points.
Vector spaces, normed spaces. Metric, continuity, convergence, analytic functions, Cauchy sequences, completeness, compactness, norm, inner product, Banach and Hilbert spaces. Best approximation of a point from a convex set, the projection theorem, the Riesz representation theorem. Introduction to linear operators, boundedness and norm, functionals, adjoint operators, unitary operators, Neumann series, resolvents. Fourier, Laplace and Z transforms. Hardy spaces and Paley-Wiener theorems. Time invariant operators and Foures-Segal theorems. Sampling and the Whittaker-Kotelnikov-Shannon theorem.
Full Syllabus
