|
This article is cited in 2 scientific papers (total in 2 papers)
Asymptotic properties of integrals of quotients when the numerator oscillates and the denominator degenerates
Sergei Kuksinabc a Institut de Mathémathiques de Jussieu–Paris Rive Gauche, CNRS, Université Paris
Diderot, UMR 7586, Sorbonne Paris Cité, F-75013, Paris, France
b School of Mathematics, Shandong University, Shanda Nanlu, 27, 250100, PRC
c Saint Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg, Russia
Abstract:
We study asymptotic expansion as $\nu\to0$ for integrals over ${ \mathbb{R} }^{2d}=\{(x,y)\}$ of quotients of the form $F(x,y) \cos(\lambda x\cdot y) \big/ \big( (x\cdot y)^2+\nu^2\big)$, where $\lambda\ge 0$ and $F$ decays at infinity sufficiently fast. Integrals of this kind appear in the theory of wave turbulence.
Key words and phrases:
asymptotic of integrals, oscillating integrals, four-waves interaction.
Received: 01.02.2018
Citation:
Sergei Kuksin
Linking options:
https://www.mathnet.ru/eng/jmag708
|
Statistics & downloads: |
Abstract page: | 248 | Full-text PDF : | 46 | References: | 28 |
|