Functional Analysis and Distribution Theory

This lecture by the instructor covers the fundamental concepts of functional analysis and distribution theory. It starts by contrasting functions and distributions, then delves into topological vector spaces, linear functionals, tempered distributions, and Schwartz' space. The importance of norms, semi-norms, and Banach spaces is discussed, along with the properties of vector spaces and operators. The lecture also explores Schwartz' functions, Gauss-Hermite functions, and the Schwartz space of test functions. Emphasis is placed on the continuity properties of linear operators and the relevance of these concepts in engineering applications.