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a New Estimate for a Trigonometric Integral of I. M. VINOGRADOV
, 1988This paper is devoted to refinements of I. M. Vinogradov's theorem on the mean. New estimates are obtained for the mean values of trigonometric sums which are effective on the domain of admissible variation of the parameters. Bibliography: 28 titles.
O. Tyrina
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The Annals of Mathematics, 1947
whose coefficients are expressed by the very well known formulas. The tests we have at our disposal for the convergence or summability of Fourier series are perfectly satisfactory for applications of Fourier series. In a number of problems we come across series which are of the form (1.1.1) without necessarily being Fourier series.
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whose coefficients are expressed by the very well known formulas. The tests we have at our disposal for the convergence or summability of Fourier series are perfectly satisfactory for applications of Fourier series. In a number of problems we come across series which are of the form (1.1.1) without necessarily being Fourier series.
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Triple trigonometric integral equations with an application
, 1980Closed form solution has been obtained for certain triple integral equations with trigonometric kernels which arise in the crack and punch problems in the linear theory of elasticity.
B. Singh +2 more
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On the integrability of trigonometric series
Analysis Mathematica, 1992пУстьϕ(t) — ФУНкцИь УНг А, УДОВлЕтВОРьУЩАь НЕ кОтОРыМ ДОпОлНИтЕльНыМ УслО ВИьМ. В РАБОтЕ ДОкАжыВАЕтс ь, ЧтО ЕслИ пОслЕДОВАт ЕльНОсть {a k } стРЕМИтсь к НУлУ И $$\mathop \Sigma \limits_{m = 0}^\infty 2^m \varphi ^{ - 1} (2^{ - m} )\varphi ^{ - 1} (\mathop \Sigma \limits_{2^m< k\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } 2^{
Dang Vu Giang, Ferenc Móricz
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A trigonometric Galerkin method for volume integral equations arising in TM grating scattering
Advances in Computational Mathematics, 2012Transverse magnetic (TM) scattering of an electromagnetic wave from a periodic dielectric diffraction grating can mathematically be described by a volume integral equation.This volume integral equation, however, in general fails to feature a weakly ...
Armin Lechleiter, Dinh-Liem Nguyen
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High asymptotic order methods for highly oscillatory integral equations with trigonometric kernels
Journal of Computational and Applied Mathematics, 2022Longbin Zhao, Qiongqi Fan, Sheng Wang
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, 2020
In this work, the buckling analysis of material sandwich plates based on a two-parameter elastic foundation under various boundary conditions is investigated on the basis of a new theory of refined trigonometric shear deformation.
Sara Chelahi Chikr +8 more
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In this work, the buckling analysis of material sandwich plates based on a two-parameter elastic foundation under various boundary conditions is investigated on the basis of a new theory of refined trigonometric shear deformation.
Sara Chelahi Chikr +8 more
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, 2019
The thermo-mechanical bending behavior of the antisymmetric cross-ply laminates is examined using a new simple four variable trigonometric plate theory. The proposed theory utilizes a novel displacement field which introduces undetermined integral terms ...
Moussa Abualnour +7 more
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The thermo-mechanical bending behavior of the antisymmetric cross-ply laminates is examined using a new simple four variable trigonometric plate theory. The proposed theory utilizes a novel displacement field which introduces undetermined integral terms ...
Moussa Abualnour +7 more
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On Summable Trigonometric Integrals
Mathematical Proceedings of the Cambridge Philosophical Society, 19311. The analogue for trigonometric integrals of de la Vallée Poussin's classical theorem concerning the uniqueness of the trigonometrical development has recently been obtained by M. Jacob in the following form.
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Integration and Trigonometric Series
2015Riemann’s previously unpublished Habilitation essay on the integration of trigonometric series was published for the first time in 1867, in an issue of the Gottingen Nachrichten that came out shortly after his death and carried several of his papers that he had left in almost a fit state to print.
Jeremy Gray, Jeremy Gray
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