Table of Contents:
  • Introduction
  • The Weyl algebra An(K)
  • Homological algebra and filtered rings
  • The rings D(V) and D̂n(K)
  • Micro-local differential operators
  • Differential operators with analytic coefficients
  • The rationality of the roots of b-functions
  • The Bernstein class of distributions and constructions of fundamental solutions to PDE's with constant coefficients
  • The representations of solutions to PDE's with constant coefficients by absolutely convergent integrals over exponential solutions.