Division of distributions

Abstract

This dissertation presents a thorough proof of L. Hörmander's theorem on the division of (tempered) distributions by polynomials. The case n = 1 is discussed in detail and serves as a motivation for the techniques that are utilized in the general case. Ali the prerequisites for Hörmander's proof (the Theorems of Seidenberg-Tarski, of Puiseaux and Whitney's Extension Theorem) are discussed in detail. As a consequence of this theorem, it follows that every non zero partial differencial operator with constant coefficients has a tempered fundamental solution. (AU)