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

2018/03/18 by Sergei Kuksin, Kuksin, Sergei · 1 citation
Economics, Econometrics and Finance · Mathematics · #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Physical sciences #Mathematical Physics (math-ph) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1803.06694

openalex publication_date 2018/03/18 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We study asymptotical expansion as \ν\→0 for integrals over \ℝ\n^2d= (x,y) of quotients of the form F(x,y) \cos(\λ x\⋅ y) \/\n\( (x\⋅ y)²+\ν²\), where \λ\≥ 0 and F decays at infinity\nsufficiently fast. Integrals of this kind appear in the theory of wave\nturbulence.\n

Cited by

• Asymptotics for a class of singular integrals of quotients with highly degenerate denominators

Related

• Asymptotics for a class of singular integrals of quotients with highly degenerate denominators
• The asymptotic behavior of degenerate oscillatory integrals in two dimensions
• Resolution of singularities, asymptotic expansions of oscillatory integrals, and related phenomena
• Oscillatory integrals with phase functions of positive real powers and asymptotic expansions
• Asymptotic estimates of oscillatory integrals with general phase and\n singular amplitude: Applications to dispersive equations