Geodesic
On invariant estimates for oscillatory integrals with polynomial phase
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 1, pp. 102-107

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In this paper we consider estimates for trigonometric (oscillatory) integrals with polynomial phase function of degree three. The main result of the paper is the theorem on uniform invariant estimates for trigonometric integrals. This estimate improves results obtained in the paper by D. A. Popov [1] for the case when the phase function is a sum of a homogeneous polynomial of third degree and a linear function, as well as the estimates of the paper [2] for the fundamental solution to the dispersion equation of third order.
Keywords: oscillatory integral, phase function
Mots-clés : amplitude, invariant, discriminant. 
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     title = {On invariant estimates for oscillatory integrals with polynomial phase},
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Akbar R. Safarov. On invariant estimates for oscillatory integrals with polynomial phase. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 1, pp. 102-107. http://geodesic.mathdoc.fr/item/JSFU_2016_9_1_a10/