Abstract
One dimensional oscillatory integrals of the type $\int^\infty _0 \xi ^\alpha \rm\exp \big[it(p(\xi )-\xi x)\big]\rm {d}\xi $ are considered, where $p(\xi )$ is a real polynomial of degree $m\geq 3$. Long-time decay and global smoothing estimates are established, as well as short-time behavior as $t\to 0$. The results are applied to the fundamental solutions of a class of linearized Kadomtsev-Petviashvili equations with higher dispersion
Citation
M. Ben-Artzi. J.-C. Saut. "Uniform decay estimates for a class of oscillatory integrals and applications." Differential Integral Equations 12 (2) 137 - 145, 1999. https://doi.org/10.57262/die/1367265625
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