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Mathematical Physics

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

Authors: Sergei Kuksin
Abstract: We study asymptotical 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.
Subjects: Mathematical Physics (math-ph)
Cite as: arXiv:1803.06694 [math-ph]
  (or arXiv:1803.06694v1 [math-ph] for this version)

Submission history

From: Sergei Kuksin [view email]
[v1] Sun, 18 Mar 2018 17:21:39 GMT (10kb)