Abstract
We consider integrals of the form
, where h is a small positive parameter and S(x, θ) and f(τ, x, θ) are smooth functions of variables τ ∈ ℝ, x ∈ ℝn, and θ ∈ ℝk; moreover, S(x, θ) is real-valued and f(τ, x, θ) rapidly decays as |τ| →∞. We suggest an approach to the computation of the asymptotics of such integrals as h → 0 with the use of the abstract stationary phase method.
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Original Russian Text © S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova, 2018, published in Matematicheskie Zametki, 2018, Vol. 103, No. 5, pp. 680–692.
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Dobrokhotov, S.Y., Nazaikinskii, V.E. & Tsvetkova, A.V. One Approach to the Computation of Asymptotics of Integrals of Rapidly Varying Functions. Math Notes 103, 713–723 (2018). https://doi.org/10.1134/S0001434618050048
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DOI: https://doi.org/10.1134/S0001434618050048