I was reading the paper
"Hörmander, L., Fourier integral operators. I, Acta Math. 127, 79-183 (1971). ZBL0212.46601." and on page 3, there is a statement saying the following thing:
Can someone explain what exactly is given by Egorov's theorem? I found the original paper by Egorov from the given reference but it is written in Russian (which I cannot read). Also, if $PA=AQ$, what is the exact relation between the principal symbols of $P$ and $Q$?