An asymptotic analysis of the Fourier-Laplace transforms of certain oscillatory functions

Frederik Broucke, Gregory Debruyne, Jasson Vindas

We study the family of Fourier-Laplace transforms $$ F_{α,β}(z)= \operatorname*{F.p.} \int_{0}^{\infty} t^β\exp(\mathrm{i} t^α-\mathrm{i} z t)\:\mathrm{d} t, \quad \operatorname*{I…