Asymptotic expansions for some integrals of quotients with degenerated divisors
We study the asymptotic expansion as ν → 0 for integrals over R 2 d = {( x , y )} of the quotients F ( x , y )/(( x · y ) 2 + ( ν Γ( x , y )) 2 ), where Γ is strictly positive and F decays at infinity sufficiently fast. Integrals of this kind appear in the description of the four-waves interactions....
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| Veröffentlicht in: | Russian journal of mathematical physics 2017-10, Vol.24 (4), p.476-487 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We study the asymptotic expansion as
ν
→ 0 for integrals over R
2
d
= {(
x
,
y
)} of the quotients
F
(
x
,
y
)/((
x
·
y
)
2
+ (
ν
Γ(
x
,
y
))
2
), where Γ is strictly positive and
F
decays at infinity sufficiently fast. Integrals of this kind appear in the description of the four-waves interactions. |
|---|---|
| ISSN: | 1061-9208 1555-6638 |
| DOI: | 10.1134/S1061920817040069 |