Positive trigonometric polynomials
, 2003 We study the boundary of the nonnegative trigonometric polynomials from the algebraic point of view. In particularly, we show that it is a subset of an irreducible algebraic hypersurface and established its explicit form in terms of resultants.
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Polynomial and trigonometric splines
, 2021 Classes of simple polynomial and simple trigonometric splines given by Fourier series are considered. It is shown that the class of simple trigonometric splines includes the class of simple polynomial splines. For some parameter values, the polynomial splines coincide with the trigonometric ones; this allows to transfer to such trigonometric splines ...
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On Some Cauchy Type Mean-Value Theorems with Applications
Communications in Advanced Mathematical SciencesSome Cauchy-type mean-value theorems for Chebychev’s inequality, Steffensen’s inequality, midpoint rule, and Simpson’s rule are presented. Furthermore, we give some applications for the obtained results using the exponential and logarithmic functions ...
Uğur Selamet Kırmacı
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Application of Chebyshev and trigonometric polynomials to the approximation of a solution of a singular integral equation with a multiplicative Cauchy kernel in the half-plane [PDF]
Opuscula Mathematica, 2008 In this article Chebyshev and trigonometric polynomials are used to construct an approximate solution of a singular integral equation with a multiplicative Cauchy kernel in the half-plane.
Paweł Karczmarek
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ON AN EXTREMAL PROBLEM FOR POLYNOMIALS WITH FIXED MEAN VALUE
Ural Mathematical Journal, 2016 Let \(T_n^+\) be the set of nonnegative trigonometric polynomials \(\tau_n\) of degree \(n\) that are strictly positive at zero. For \(0\le\alpha\le2\pi/(n+2),\) we find the minimum of the mean value of polynomial \((\cos\alpha-\cos{x})\tau_n(x)/\tau_n(0)
Alexander G. Babenko
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Equivalence between various Shape Preserving Approximations of periodic functions
Researches in MathematicsWe show that the validity of Jackson-type estimates in comonotone and coconvex approximations of continuous $2\pi$-periodic functions by trigonometric polynomials is equivalent to the validity of the corresponding estimates of approximation by continuous
D. Leviatan, O.V. Motorna, I.O. Shevchuk
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Integral inequalities for trigonometric polynomials in periodic Morrey spaces
Современная математика: Фундаментальные направленияIn this paper, we present a detailed exposition of Bernstein’s inequality, inequalities of different metrics and different dimensions for trigonometric polynomials in periodic Morrey spaces.
D. J. Joseph
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THREE-VARIABLE ALTERNATING TRIGONOMETRIC FUNCTIONS AND CORRESPONDING FOURIER TRANSFORMS
Acta Polytechnica, 2016 The common trigonometric functions admit generalizations to any higher dimension, the symmetric, antisymmetric and alternating ones. In this paper, we restrict ourselves to three dimensional generalization only, focusing on alternating case in detail ...
Agata Bezubik, Severin Pošta
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Orthogonal sets of data windows constructed from trigonometric polynomials [PDF]
Suboptimal, easily computable substitutes for the discrete prolate-spheroidal windows used by Thomson for spectral estimation are given.
Greenhall, C. A.
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Approximation of classes B^ω_p,θ of periodic functions of several variables by polynomials with spectrum from cubic areas (in Ukrainian) [PDF]
Математичні Студії, 2011 We have obtained exact order estimates for error of approximation of classes B^ω_p,θ of periodic functions of several variables by trigonometric polynomials with spectrum from cubic areas.
S. A. Stasyuk
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