Convolution and Fourier Transform

This lecture covers the definition of convolution, its basic properties, and its application to the heat equation. The physical discussion includes similarities and differences between heat, wave, and Schrödinger equations. The lecture also defines dual space, tempered distributions, weak convergence, and adjoint operator. Examples of tempered distributions like delta function and integration against polynomially bounded functions are provided. The lecture concludes with the definition of the Fourier transform on tempered distributions.