synthetic differential geometry
Introductions
from point-set topology to differentiable manifolds
geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeometry
Differentials
Tangency
The magic algebraic facts
Theorems
Axiomatics
Models
differential equations, variational calculus
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
(properly supported peudo-differential operator)
A pseudo-differential operator on a manifold is called properly supported if for each compact subset there exists a compact subset such that for a distribution with support in it follows that the derivative of distributions has support in
and such that
(Hörmander 85 (18.1.21) recalled e.g. in Radzikowski 96. p. 8,9)
(differential operators are properly supported pseudo-differential operators)
Every ordinary differential operator , regarded as a pseudo-differential operator, is properly supported (def. ), since differential operators do not increase the support of the functions they act on:
Johann Duistermaat, Lars Hörmander, Fourier integral operators II, Acta Mathematica 128, 183-269, 1972 (Euclid)
Lars Hörmander, The analysis of partial differential operators III, Springer 1985
Marek Radzikowski, Micro-local approach to the Hadamard condition in quantum field theory on curved space-time, Commun. Math. Phys. 179 (1996), 529–553 (Euclid)
Last revised on November 23, 2017 at 12:49:27. See the history of this page for a list of all contributions to it.