Approximation Of Fourier Series Research Articles

On approximation of double Fourier series and its conjugate series for functions in mixed Lebesgue space

In this paper, we study the approximation of double Fourier series and its conjugate series for functions in mixed Lebesgue space Lp, p ∈ [1,∞]2 using double Karamata Kλ,μ means.

On the degree of approximation of Fourier series based on a certain class of product deferred summability means

In this article, we first introduce and study the basic concepts of deferred Euler and deferred Nörlund product summability means of Fourier series of arbitrary periodic functions. We then estimate the degree of approximation of Fourier series of an arbitrary periodic function in the generalized Zygmund class based upon our proposed product deferred summability means. Moreover, we discuss some important concluding remarks in connection with our findings. Finally, we suggest a direction for future studies on this subject, which are based upon the basic notion of statistical product deferred summability means of Fourier series of arbitrary periodic functions in the generalized Zygmund class.

Approximation of Fourier Series of Functions in Besov Space by Borel Means

In the present article, a result on degree of approximation of Fourier series of functions in the Besov space by Borel mean is established.

Dynamic stability of hybrid fiber/nanocomposite-reinforced toroidal shells subjected to the periodic axial and pressure loadings

In this article, the dynamic instability of the hybrid fiber/nanocomposite-reinforced toroidal shells is investigated. By using the approximation of Fourier series and applying the Galerkin method, a semi-analytical solution is achieved. The proposed method provides an accurate assessment of the dynamic stability of the shell with no computational costs in comparison to the numerical methods. By comparing the obtained results for some examples with those available in the present literature, the accuracy of present formulation is approved. In order to evaluate the effects of geometrical and mechanical specifications on the dynamic instability of the proposed shells, a comprehensive parametric study is performed, as well.

On degree of approximation of Fourier series of functions in Besov space using Nörlund mean

In the present article, we have established a result on degree of approximation of function in the Besov space by (N; rn)- mean of Trigonometric Fourier series

Free vibration and stability of hybrid nanocomposite-reinforced shallow toroidal shells using an extended closed-form formula based on the Galerkin method

This paper presents an analytical solution for free-vibration and stability analyses of hybrid-composite toroidal shells. The considered hybrid material incorporates the composition of fibers and nanocomposite-reinforced matrix (NCRM) such as carbon nanotubes (CNTs) and graphene nanoplatelets (GPLs). The governing differential equations are extended based on the first-order transverse shear deformation theory (FSDT) and are solved by employing the approximation of Fourier series and Galerkin method. The considered hybrid composite material in the parametric studies are consisted of three layers in which the polymeric matrix are reinforced by CNTs in some layers and reinforced by GPLs in the other layers.

Approximation of Fourier series in terms of functions in $L_p$ Spaces for $0

Many results introduced for the absolutely convergence of Fourier series in terms of absolutely continuous functions. Here we study the convergence of Fourier series in terms of $p$-integrable functions series.

Degree of approximation of Fourier series of functions in Besov space by deferred Nörlund mean

In the present paper, we estimate the rate of convergence of Fourier series of functions by Deferred Nörlund mean in Besov space which is a generalization of [Formula: see text] space.

Degree of approximation of signals in certain Lipschitz classes by the Zweier–Euler product summability method of Fourier series

The paper introduces the notion of a new product summability method, which is obtained by superimposing the Zweier method on the Euler method. This method is applied to obtain the degree of approximation of Fourier series of signals (functions) belonging to certain Lipschitz classes.

On approximation of hexagonal Fourier series in the generalized Hölder metric

Let $f$ be an $H$-periodic continuous function. The approximation order of the function $f$ by deferred Cesaro means of its hexagonal Fourier series is estimated in uniform and generalized H\"{o}lder metrics.

Asymptotics of approximation of continuous periodic functions by linear means of their Fourier series

We establish an asymptotic formula for the rate of approximation of Fourier series of individual periodic functions by linear averages with an error , . This formula is applicable to the means of Riesz, Gauss–Weierstrass, Picard and others. The result is new even for the arithmetic means of partial Fourier sums. We use the formula to determine the asymptotic behaviour of functions in a certain class. Separately, we consider the case of positive integral convolution operators.

A Study on Degree of Approximation by Product Means of the Fourier Series in a W (Lr, ξ(t))( r ≥ 1) Class

The purpose of present paper is to approach a new result on degree of approximation of Fourier series of a function f ∈ W (Lr, ξ(t)) class by C2Tn product summability. So many work have been done for approximation of Fourier series and its conjugate series but this work is yet not seen for (C2Tn) product summability.

Strong approximation of Fourier series on generalized periodic Morrey spaces

Strong approximation of Fourier series on generalized periodic Morrey spaces

Stability and Control of Tailless Aircraft Using Variable-Fidelity Aerodynamic Analysis

The purpose of this study is to evaluate the stability and control characteristics of the tailless aircraft using a hierarchy of variable-fidelity aerodynamics analysis methods, including unsteady linear potential flow, Euler, and Reynolds-averaged Navier–Stokes solvers as low-, medium-, and high-fidelity analysis, respectively. Contributions of the study are numerous. First, derivations of the equations of motion for the tailless aircraft and stability criteria using system matrices in longitudinal and lateral motions were carried out. Second, an efficient time-spectral Reynolds-averaged Navier–Stokes computational fluid dynamics method, which is based on the solution approximation of a discrete Fourier series, and the steady form of a corresponding adjoint solution approach can compute dynamic derivatives at computational cost considerably less than that of the conventional time-marching method without deterioration in solution accuracy. The innovative control effector 101 configuration was chosen, and the validation of the variable-fidelity computation results was made with wind tunnel data for forces, moments, and their derivative values in static and dynamic motions. Finally, example flight conditions of trim, climb, and side slip motions were analyzed by the Reynolds-averaged Navier–Stokes solver for the stability analysis. It is concluded that the weak instabilities observed in some of the dynamic modes can be easily controlled by appropriate control inputs.

Groups of Deviations of the Fourier Series in Generalized Hölder Spaces

We study the rate of convergence of the values of analogs of the functionals of strong approximation of Fourier series in generalized L-Holder spaces.

Approximation of Fourier Series of a function of Lipchitz class by Product Means

Approximation of Fourier Series of a function of Lipchitz class by Product Means

Degree of Approximation of Fourier series of function of bounded variation by (Z, , ) method

Degree of Approximation of Fourier series of function of bounded variation by (Z, , ) method

Degree of approximation of Fourier series by (E,r)(N,p,q) means

Degree of approximation of Fourier series by (E,r)(N,p,q) means

Applications of general monotone sequences to strong approximation by Fourier series

We consider the strong means of Fourier series generated by infinite nonnegative triangular matrices and prove some estimates of such means in the case of a matrix with rows stating the sequences from the class GM(5β). Our theorems correspond to the results of L. Leindler [L. Leindler, A note on strong approximation of Fourier series, Anal. Math. 29 (2003) 195–199] and essentially extend the result of S.M. Mazhar and V. Totik [S.M. Mazhar, V. Totik, Approximation of continuous functions by T -means of Fourier series, J. Approx. Theory, 60 (1990) 174–182].

Lebesgue type points in strong (C,α) approximation of Fourier series

We present an estimation of the $H_{k_{0},k_{r}}^{q,\alpha }f$ and $H_{\lambda,u}^{\phi,\alpha }f$ means as approximation versions of the Totik type generalization (see [5], [6]) of the result of G. H. Hardy, J. E. Littlewood. Some cor