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.
This work is supported by the grant of the Republic of Uzbekistan, grant F-4-17.
Received: 17.04.2015 Received in revised form: 10.11.2015 Accepted: 21.12.2015
Bibliographic databases:
Document Type:
Article
UDC:517.518.5
Language: English
Citation:
Akbar R. Safarov, “On invariant estimates for oscillatory integrals with polynomial phase”, J. Sib. Fed. Univ. Math. Phys., 9:1 (2016), 102–107
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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
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\crossref{https://doi.org/10.17516/1997-1397-2016-9-1-102-107}
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This publication is cited in the following 7 articles:
I. A. Ikromov, A. R. Safarov, “O ravnomernykh otsenkakh ostsillyatornykh integralov s gladkoi fazoi”, Chebyshevskii sb., 25:1 (2024), 42–51
I. A. Ikromov, A. R. Safarov, A. T. Absalamov, “Ob otsenke trigonometricheskikh integralov s kvadratichnoi fazoi”, Chebyshevskii sb., 25:1 (2024), 52–61
Akbar R. Safarov, Ulugbek A. Ibragimov, “Oscillatory integrals for Mittag–Leffler functions”, Zhurn. SFU. Ser. Matem. i fiz., 17:4 (2024), 488–496
Isroil A. Ikromov, Michael Ruzhansky, Akbar R. Safarov, “Oscillatory integrals for Mittag-Leffler functions with two variables”, Comptes Rendus. Mathématique, 362:G7 (2024), 789
Isroil A. Ikromov, Akbar R. Safarov, “Estimates for Integrals with Mittag-Leffler Functions”, Lobachevskii J Math, 45:8 (2024), 3884
Akbar R. Safarov, “Uniform estimates for Mittag–Leffler functions with smooth phase”, Zhurn. SFU. Ser. Matem. i fiz., 16:5 (2023), 673–680
Akbar R. Safarov, “Estimates for Mittag-Leffler functions with smooth phase depending on two variables”, Zhurn. SFU. Ser. Matem. i fiz., 15:4 (2022), 459–466
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