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Asymptotic analysis of oscillatory integrals via the Newton polyhedra of the phase and the amplitude

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arxiv 1203.0808 v1 pith:OLQXTXES submitted 2012-03-05 math.CA math.CV

Koji Cho , Joe Kamimoto , Toshihiro Nose This is my paper · ORCID
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keywords amplitudeintegralsoscillatoryphaseasymptoticbehaviornewtonpolyhedra
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The asymptotic behavior at infinity of oscillatory integrals is in detail investigated by using the Newton polyhedra of the phase and the amplitude. We are especially interested in the case that the amplitude has a zero at a critical point of the phase. The properties of poles of local zeta functions, which are closely related to the behavior of oscillatory integrals, are also studied under the associated situation.

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  1. Subtlety of oscillation indices of oscillatory integrals of real analytic functions

    math.CV 2025-11 reject novelty 4.0 of 10

    For real analytic homogeneous functions that are Newton R-nondegenerate and convenient, the paper claims a strict inequality (even n) or equality (odd n) between the absolute oscillation index and the real log canonic...

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