# Fourier integral operator

1. Sep 5, 2014

### super_al57

Hi! I have a question for you. At the end of the post there's a link. There's the homework which I have to do for an exam. I have to study the Fourier Integral Operator that there is at the begin of the paper. I did almost all the homework but I can't do a couple of things. First: at the point 1, using k-times the integration by parts, I have to prove that |eiψ/l(tL)kau|=O(<θ>m-δN).
Second: at the end I have to estimate $\partial^\alpha\varphi$ derivating the eikonal equation but I don't know how to begin.

http://freepdfhosting.com/08103fe65b.pdf