The stationary phase method and pseudodifferential operators

In the paper asymptotic expansions are calculated for integrals
$$ \int f(x)\exp(i\lambda g(x))dx,\qquad\lambda\to+\infty, $$
of rapidly oscillating functions, in which $x\in R^n$, $f$ and $g$ are smooth functions, and $g$ is real-valued. The results obtained serve to develop a calculus of pseudodifferential operators and generalizations of them, the Fourier integral operators.