Asymptotic Properties of Integrals of Quotients when the Numerator Oscillates and the Denominator Degenerates - Kuksin, S. (Журнал математической физики, анализа, геометрии, 2018)
We study asymptotic expansion as ν→0 for integrals over ℝ²d={(x,y)} of quotients of the form F(x,y)cos(λx∙y)/((x∙y)²+ν²), where λ≥0 and F decays at infinity sufficiently fast. Integrals of this kind appear in the theory of wave turbulence.