APPROXIMATION PROPERTIES OF SOME DISCRETE FOURIER SUMS FOR PIECEWISE SMOOTH DISCONTINUOUS FUNCTIONS
Проблемы анализа, 2019 Denote by Ln, N (f, x) a trigonometric polynomial of order at most n possessing the least quadratic deviation from f with respect to the system tk = u + 2πk N N−1 k=0 , where u ∈ R and n 6 N/2.
G. G. Akniyev
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Some applications of the Menshov–Rademacher theorem
Comptes Rendus. Mathématique, 2021 Given a sequence $(X_n)$ of real or complex random variables and a sequence of numbers $(a_n)$, an interesting problem is to determine the conditions under which the series $\sum _{n=1}^\infty a_n X_n$ is almost surely convergent.
Mukeru, Safari
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DISCRETE LEAST SQUARES APPROXIMATION OF PIECEWISE-LINEAR FUNCTIONS BY TRIGONOMETRIC POLYNOMIALS
Проблемы анализа, 2017 Let N be a natural number greater than 1. Select N uniformly distributed points t_k = 2πk/N (0 ≤ k ≤ N − 1) on [0, 2π]. Denote by L_{n,N} (f) = L_{n,N} (f, x) (1 ≤ n ≤ N/2) the trigonometric polynomial of order n possessing the least quadratic deviation ...
G. G. Akniyev
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Hardy-Littlewood theorem for series with general monotone coefficients
Қарағанды университетінің хабаршысы. Математика сериясы, 2018 In this work we study trigonometric series with general monotone coefficients. Also, we consider Lqϕ ( Lq ) space. In particular, when ϕ ( t ) ≡ 1 the space Lqϕ ( Lq ) coincides with Lq .
S. Bitimkhan
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On Divergence of Fourier Series by Some Methods of Summability
Journal of Function Spaces and Applications, 2012 A new summability method of series is introduced and studied. The particular cases of this method are, for example, variable-order Cesaro and Riesz methods. Applications to divergence problem of Fourier series are given.
Shakro Tetunashvili
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Divergent series and generalized mixed problem for wave equation [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. ИнформатикаAllowing the inversion of the operations of summation and integration for trigonometric Fourier series we present the solution by Fourier method of the generalized mixed problem for the homogeneous wave equation with zero initial velocity and fixed ends ...
Khromov, August Petrovich
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Concerning the multiplicators of fourier series in the trigonometric system [PDF]
Mathematical Notes, 1998 The author proves two theorems on the boundedness (in the norm of \(L_p(\mathbb{T}^n)\)) of the partial sums of Fourier series and three theorems on Fourier multipliers in \(L_p(\mathbb{T}^n)\). As a pattern, here we present Theorem 5.
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Approximation of functions by (C,2)(E,1) product summability method of Fourier series
Ratio Mathematica, 2020 Various investigators such as Leindler [10], Chandra [1], Mishra et al. [7], Khan [11], Kushwaha [6] have determined the degree of approximation of 2 pai-periodic functions belonging to generalized Lipschitz class of functions through trigonometric ...
Jitendra Kumar Kushwaha
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Estimation of the difference of partial sums of expansions by the root functions of the differential operator and into trigonometric Fourier series [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. ИнформатикаWe consider a linear ordinary differential operator defined by an $n$-th order differential expression with a nonzero coefficient for $(n-1)$th derivative and Birkhoff regular two-point boundary conditions.
Rykhlov, Victor Sergeyevich
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The problem of trigonometric Fourier series multipliers of classes in λp,q spaces
Қарағанды университетінің хабаршысы. Математика сериясы, 2020 In this article, we consider weighted spaces of numerical sequences λp,q, which are defined as sets of sequences a = {ak}∞k=1, for which the norm ||a||λp,q := (∞Σk=1|ak|qkq/p −1)1/q < ∞ is finite. In the case of non-increasing sequences, the norm of the
A. Bakhyt, N.T. Tleukhanova
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