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J. Sib. Fed. Univ. Math. Phys., 2016, Volume 9, Issue 1, Pages 102–107 (Mi jsfu464)  

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.

Funding Agency Grant Number
Academy of Sciences of the Republic of Uzbekistan F-4-17
This work is supported by the grant of the Republic of Uzbekistan, grant F-4-17.


DOI: https://doi.org/10.17516/1997-1397-2016-9-1-102-107

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Bibliographic databases:

UDC: 517.518.5
Received: 17.04.2015
Received in revised form: 10.11.2015
Accepted: 21.12.2015
Language:

Citation: Akbar R. Safarov, “On invariant estimates for oscillatory integrals with polynomial phase”, J. Sib. Fed. Univ. Math. Phys., 9:1 (2016), 102–107

Citation in format AMSBIB
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\by Akbar~R.~Safarov
\paper On invariant estimates for oscillatory integrals with polynomial phase
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2016
\vol 9
\issue 1
\pages 102--107
\mathnet{http://mi.mathnet.ru/jsfu464}
\crossref{https://doi.org/10.17516/1997-1397-2016-9-1-102-107}
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