Asymptotic Properties of Integrals of Quotients when the Numerator Oscillates and the Denominator Degenerates
We study asymptotic expansion as ν→0 for integrals over ℝ²d={(x,y)} of quotients of the form F(x,y)cos(λx∙y)/((x∙y)²+ν²), where λ≥0 and F decays at infinity sufficiently fast. Integrals of this kind appear in the theory of wave turbulence.
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| Datum: | 2018 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2018
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| Schriftenreihe: | Журнал математической физики, анализа, геометрии |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/145883 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Asymptotic Properties of Integrals of Quotients when the Numerator Oscillates and the Denominator Degenerates / S. Kuksin // Журнал математической физики, анализа, геометрии. — 2018. — Т. 14, № 4. — С. 510-518. — Бібліогр.: 3 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We study asymptotic expansion as ν→0 for integrals over ℝ²d={(x,y)} of quotients of the form F(x,y)cos(λx∙y)/((x∙y)²+ν²), where λ≥0 and F decays at infinity sufficiently fast. Integrals of this kind appear in the theory of wave turbulence. |
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