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This article is cited in 6 scientific papers (total in 6 papers)
On invariant estimates for oscillatory integrals with polynomial phase
Akbar R. Safarov Samarkand State University, Universitetsky boulevard, 15, 140104, Samarkand, Uzbekistan
Abstract:
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, amplitude, invariant, discriminant.
Received: 17.04.2015 Received in revised form: 10.11.2015 Accepted: 21.12.2015
Citation:
Akbar R. Safarov, “On invariant estimates for oscillatory integrals with polynomial phase”, J. Sib. Fed. Univ. Math. Phys., 9:1 (2016), 102–107
Linking options:
https://www.mathnet.ru/eng/jsfu464 https://www.mathnet.ru/eng/jsfu/v9/i1/p102
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Abstract page: | 194 | Full-text PDF : | 68 | References: | 29 |
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