Asymptotic expansions for a class of singular integrals emerging in non-linear wave systems

Andrey Dymov

We find asymptotical expansions as $\nu \to 0$ for integrals of the form ${\int }_{{\mathbb{R}}^d}F(x)/(\omega (x{)}^2+{\nu }^2)dx$, where sufficiently smooth functions $F$ and $\omega$ sati…