This entry is about Hörmander’s criterion on wave front sets. This is different from “Hörmander's condition” on tangent vector fields.
The Hörmander criterion (Hörmander 90, theorem 8.2.10) says that the product of two distributions (on some manifold ) is well-defined if their wave front sets are such that for a covector contained in one of the two wave front sets then the covector with the opposite direction in not contained in the other wave front set, i.e. the intersection fiber product inside the cotangent bundle of the pointwise sum of wave fronts with the zero section is empty:
i.e.
See at product of distributions for details.
Lars Hörmander, Fourier integral operators. I. Acta Mathematica 127, 79–183 (1971) (Euclid)
Lars Hörmander, section 8.1 of The analysis of linear partial differential operators, vol. I, Springer 1983, 1990
Last revised on December 22, 2017 at 20:38:52. See the history of this page for a list of all contributions to it.