Fourier Transformation: Fundamentals

This lecture covers the fundamentals of the Fourier transformation, including decreasing causal exponential signals, functions of the Schwartz class, Parseval relation, weak convergence, and the Fourier transformation in the sense of distributions. It also discusses the classical framework for the Fourier transformation, the Schwartz class of functions, and the invertibility of the Fourier transformation. The lecture explores the concept of distributions, scalar products, and the generalized Fourier transformation. Additionally, it delves into the change of scale, fundamental properties, and the definition of the Fourier transformation in the sense of distributions, with a practical application on the scaling of the Dirac pulse.