Distributions & Interpolation Spaces

This lecture covers the concept of distributions and interpolation spaces, focusing on the definition of vector spaces of all continuous functions with compact support. It explains the necessity of endowing spaces with a topological structure to discuss convergence. The lecture delves into the convergence of sequences and the space of distributions, emphasizing the smoothness and wild elements contained within. It also introduces the concept of the dual space of distributions and discusses convergence in different spaces. The lecture concludes with examples of distributions and the notion of order and derivatives of distributions.