A smooth introduction to the wavefront set
Résumé
The wavefront set of a distribution describes not only the points where the
distribution is singular, but also the ‘directions’ of the singularities. Because of
its ability to control the product of distributions, the wavefront set was a key
element of recent progress in renormalized quantum field theory in curved
spacetime, quantum gravity, the discussion of time machines or quantum
energy inequalitites. However, the wavefront set is a somewhat subtle concept
whose standard definition is not easy to grasp. This paper is a step-by-step
introduction to the wavefront set, with examples and motivation. Many different
definitions and new interpretations of the wavefront set are presented.
Some of them involve a Radon transform.