In microlocal analysis, the propagation of singularities theorem (also called the Duistermaat–Hörmander theorem) is theorem which characterizes the wavefront set of the distributional solution of the partial (pseudo) differential equation for a pseudodifferential operator
on a smooth manifold.
It says that the propagation of singularities follows the bicharacteristic flow of the principal symbol of
The theorem appeared 1972 in a work on Fourier integral operators by Johannes Jisse Duistermaat and Lars Hörmander and since then there have been many generalizations which are known under the name propagation of singularities.
be a properly supported pseudodifferential operator of class
with a real principal symbol
, which is homogeneous of degree
be a distribution that satisfies the equation
is invariant under the Hamiltonian flow induced by