CHAPTER III - THE FUNDAMENTAL SOLUTIONS

Abstract

This chapter discusses the fundamental solutions. It describes the standard situation of a pseudo-Riemannian manifold (M,g) whose metric has Lorentz signature. The chapter provides an overview of reciprocity for formally self-adjoint operators. From the general theory of Cauchy's problem it is known that one can determine the higher derivatives of a possible solution on the initial surface. The Hadamard coefficients were introduced in the fundamental papers. “Transport equations” similar to the differential equations arise if one applies the various methods for obtaining asymptotic solutions of hyperbolic differential equations.