Journal of the Mathematical Society of Japan

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

Koji CHO, Joe KAMIMOTO, and Toshihiro NOSE

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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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J. Math. Soc. Japan, Volume 65, Number 2 (2013), 521-562.

First available in Project Euclid: 25 April 2013

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Zentralblatt MATH identifier

Primary: 58K55: Asymptotic behavior
Secondary: 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx] 14M25: Toric varieties, Newton polyhedra [See also 52B20]

oscillatory integrals oscillation index and its multiplicity local zeta function asymptotic expansion Newton polyhedra of the phase and the amplitude essential set


CHO, Koji; KAMIMOTO, Joe; NOSE, Toshihiro. Asymptotic analysis of oscillatory integrals via the Newton polyhedra of the phase and the amplitude. J. Math. Soc. Japan 65 (2013), no. 2, 521--562. doi:10.2969/jmsj/06520521.

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