ABSTRACT
In this chapter, we try to convey the essence of the basic concept of a fundamental solution of the heat equation. This is a solution from which other solutions can be generated by means of an integral transform acting on functions and signed measures, and the results presented here are used repeatedly throughout the book. In section 6, which does not contain any proofs, we outline the corresponding situation for more general second order, linear, parabolic, partial differential equations, and describe how far the results and methods of sections 1 to 5 can be generalized.
