We consider integrals of the form
$$Ileft( {x,h} right) = frac{1}{{{{left( {2pi h} right)}^{k/2}}}}int_{{mathbb{R}^k}} {fleft( {frac{{Sleft( {x,theta } right)}}{h},x,theta } right)} dtheta $$
, where
h is a small positive parameter and
S(
x,
θ) and
f(
τ,
x,
θ) are smooth functions of variables
τ ∈ ?,
x ∈ ?
n , and
θ ∈ ?
k ; moreover,
S(
x,
θ) is real-valued and
f(
τ,
x,
θ) rapidly decays as |
τ| →∞. We suggest an approach to the computation of the asymptotics of such integrals as
h → 0 with the use of the abstract stationary phase method.
