An accuracy improvement in Egorov's theorem.
We prove that the theorem of Egorov, on the canonical transformation of symbols of pseudodifferential operators conjugated by Fourier integral operators, can be sharpened. The main result is that the statement of Egorov's theorem remains true if, instead of just considering the principal symbols in S/S for the pseudodifferential operators, one uses refined principal symbols in S/S, which for classical operators correspond simply to the principal plus the subprincipal symbol, and can generally be...