Topic
Fourier series
About: Fourier series is a research topic. Over the lifetime, 16548 publications have been published within this topic receiving 322486 citations.
Papers published on a yearly basis
Papers
More filters
IBM1
TL;DR: It is shown that a section of a scattering function vs scattering angle curve can be adequately represented by a fourier series with less than 2x + 10 terms.
Abstract: Results of computations are presented to show the variations of coefficients of four different Legendre series, one for each of the four scattering functions needed in describing directional dependence of the radiation scattered by a sphere. Values of the size parameter (x) covered for this purpose vary from 0.01 to 100.0. An adequate representation of the entire scattering function vs scattering angle curve is obtained after making use of about 2x + 10 terms of the series. It is shown that a section of a scattering function vs scattering angle curve can be adequately represented by a fourier series with less than 2x + 10 terms. The exact number of terms required for this purpose depends upon values of the size parameter and refractive index, as well as upon the values of the scattering angles defining the section under study. Necessary expressions for coefficients of such fourier series are derived with the help of the addition theorem of spherical harmonics.
62 citations
Book•
01 Jan 2011
TL;DR: The Dirac delta function as discussed by the authors is a generalised Dirac function with time-invariant linear systems and its derivatives, which is a type of generalised functions. Introduction to distributions Integration theory and generalized functions Solutions References Index.
Abstract: Results from elementary analysis The Dirac delta function Properties of the delta function and its derivatives Time-invariant linear systems The Laplace Transform Fourier Series and Fourier transforms Other types of generalised functions Introduction to distributions Integration theory NSA and generalised functions Solutions References Index.
62 citations
TL;DR: In this article, the authors studied the divergence properties of the Fourier series on Cantortype fractal measures, and showed that in some cases the L 1-norm of the corresponding Dirichlet kernel grows exponentially fast.
Abstract: We study divergence properties of the Fourier series on Cantortype fractal measures, also called the mock Fourier series. We show that in some cases the L1-norm of the corresponding Dirichlet kernel grows exponentially fast, and therefore the Fourier series are not even pointwise convergent. We apply these results to the Lebesgue measure to show that a certain rearrangement of the exponential functions, with affine structure, which we call a scrambled Fourier series, have a corresponding Dirichlet kernel whose L1norm grows exponentially fast, which is much worse than the known logarithmic bound. The divergence properties are related to the Mahler measure of certain polynomials and to spectral properties of Ruelle operators.
62 citations
TL;DR: In this paper, the buckling problem of thin rectangular functionally graded plates subjected to proportional biaxial compressive loadings with arbitrary edge supports is investigated, and a classical plate theory based on the physical neutral plane is applied to derive the stability equations.
Abstract: In this paper, the buckling problem of thin rectangular functionally graded plates subjected to proportional biaxial compressive loadings with arbitrary edge supports is investigated Classical plate theory (CPT) based on the physical neutral plane is applied to derive the stability equations Mechanical properties of the FGM plate are assumed to vary continuously along its thickness according to a power law function The displacement function is considered to be in the form of a double Fourier series whose derivatives are determined using Stokes' transformation The advantage of this method is capability of considering any possible combination of boundary conditions with no necessity to be satisfied in the Fourier series To give generality to the problem, the plate is assumed to be elastically restrained by means of rotational and translational springs at the four edges Numerical examples are presented, and the effects of the plate aspect ratio, the FGM power index, and the loading proportionality factor on the buckling load of an FGM plate with different usual boundary conditions are studied The present results are compared with those have been previously reported by other analytical and numerical methods, and very good agreement is seen between the findings indicating validity and accuracy of the proposed approach in the buckling analysis of FGM plates
61 citations
TL;DR: In this article, the approximation properties of Norlund (Nn) and Riesz (Rn) means of trigono- metric Fourier series were investigated in generalized Lebesgue spaces.
Abstract: The approximation properties of Norlund (Nn) and Riesz (Rn) means of trigono- metric Fourier series are investigated in generalized Lebesgue spaces L p(x) . The deviations � f −Nn(f)� p(x) andf −Rn(f)� p(x) are estimated by n −α for f ∈ Lip(α,p(x)) (0 < α 1).
61 citations