Geodesic
Asymptotic properties of integrals of quotients when the numerator oscillates and the denominator degenerates
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 14 (2018) no. 4 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{JMAG_2018_14_4_a3,
     author = {Sergei Kuksin},
     title = {Asymptotic properties of integrals of quotients when the numerator oscillates and the denominator degenerates},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     year = {2018},
     volume = {14},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2018_14_4_a3/}
}
TY  - JOUR
AU  - Sergei Kuksin
TI  - Asymptotic properties of integrals of quotients when the numerator oscillates and the denominator degenerates
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2018
VL  - 14
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/JMAG_2018_14_4_a3/
LA  - en
ID  - JMAG_2018_14_4_a3
ER  - 
%0 Journal Article
%A Sergei Kuksin
%T Asymptotic properties of integrals of quotients when the numerator oscillates and the denominator degenerates
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2018
%V 14
%N 4
%U http://geodesic.mathdoc.fr/item/JMAG_2018_14_4_a3/
%G en
%F JMAG_2018_14_4_a3
Sergei Kuksin. Asymptotic properties of integrals of quotients when the numerator oscillates and the denominator degenerates. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 14 (2018) no. 4. http://geodesic.mathdoc.fr/item/JMAG_2018_14_4_a3/

[1] Math. Notes, 103 (2018), 713–723 | DOI | DOI | MR | Zbl

[2] S. Kuksin, “Asymptotic expansions for some integrals of quotients with degenerated divisors”, Russ. J. Math. Phys., 24 (2017), 476–487 | DOI | MR | Zbl

[3] S. Nazarenko, Wave Turbulence, Lecture Notes in Physics, 825, Springer, Heidelberg, 2011 | DOI | MR | Zbl