I have been reading Semi-classical analysis by Guillemin and Sternberg. At the end of Chapter 8, they gave an abstract version of the stationary phase method. I have a hard time figuring out what $a\_i$ in the asymptotic expansion of theorem 8.14.1 are. Any suggestions are welcomed.



Abstract stationary phase
the $a\_i$'s are complex coefficients in the asymptotic expansion $a(h)=\sum\_{i=0}^\infty a\_i h^i$; a more explicit expression is given on page 275-276 of [Guillemin and Sternberg:](http://www.math.harvard.edu/~shlomo/docs/Semi_Classical_Analysis_Start.pdf)


![](https://ilorentz.org/beenakker/MO/asymptotic.png)


