MATH 654 Generalized Functions and PDE
L. Schwartz spaces of infinitely differentiable functions, convolution operation, partition of unity. Dual spaces and differential operators on generalized functions. Fourier transforms on generalized functions, fundamental solution for a linear differential equation, existence of a general solution, application to Laplace equations. Approximation of generalized functions by infinitely differentiable functions. Kernel theorem and its applications. Prerequisite: 625 or 653.