Asymptotic properties of integrals of quotients when the numerator oscillates and the denominator degenerates

Sergei Kuksin

Geodesic

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Asymptotic properties of integrals of quotients when the numerator oscillates and the denominator degenerates

Sergei Kuksin

Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 14 (2018).

Voir la notice de l'article provenant de la source Math-Net.Ru

Résumé

We study asymptotic expansion as

ν \to 0

for integrals over

R^{2 d} = {(x, y)}

of quotients of the form

F (x, y) \cos (λ x \cdot y) / ((x \cdot y)^{2} + ν^{2})

, where

λ \geq 0

and

F

decays at infinity sufficiently fast. Integrals of this kind appear in the theory of wave turbulence.

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@article{JMAG_2018_14_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},
     publisher = {mathdoc},
     volume = {14},
     year = {2018},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/JMAG_2018_14_a3/}
}

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PY  - 2018
VL  - 14
PB  - mathdoc
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%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
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%F JMAG_2018_14_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). https://geodesic-test.mathdoc.fr/item/JMAG_2018_14_a3/

Bibliographie
Cité par

[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