Distributions & Interpolation Spaces

This lecture covers the definition and properties of the convolution operator between functions, emphasizing linearity, commutativity, and associativity. It explores the convolution operator between functions in different function spaces, discussing their linearity and compact support. The lecture also delves into the concept of interpolation spaces and their applications in defining convolution operators. The instructor demonstrates the continuity and compactness of the convolution operator, providing proofs and examples to illustrate the theoretical concepts. The lecture concludes with a discussion on the convergence of functions in different function spaces and the implications of compact support in function analysis.