We consider expansions of smooth, nonperiodic functions defined on compact intervals in eigenfunctions of polyharmonic operators equipped with homogeneous Neumann boundary conditions. Having determined asymptotic expressions for both the eigenvalues and eigenfunctions of these operators, we demonstrate how these results can be used in the efficient computation of expansions. Next, we consider t...

A new formulation of the differential method in TM polarization, based on correct representation of truncated Fourier series of products of discontinuous functions, is proposed. Although the derived equations are more complicated than in the classical formulation, the convergence rate with respect to the truncation parameter (with the number of diffraction orders taken into account) is much fas...

In this paper, we propose a new residual analysis method using Fourier series transform into fuzzy time series model for improving the forecasting performance. This hybrid model takes advantage of the high predictable power of fuzzy time series model and Fourier series transform to fit the estimated residuals into frequency spectra, select the low-frequency terms, filter out high-frequency term...

we consider gabor systems generated by a gaussian function and prove certain classical results of paley and wiener on nonharmonic fourier series of complex exponentials for the gabor expansion‎. ‎in particular, we prove a version of plancherel-po ́lya theorem for entire functions with finite order of growth and use the hadamard factorization theorem to study regularity‎, ‎exactness and deficienc...

the computational method based on using the operational matrix of anorthogonal function for solving variational problems is computeroriented. in this approach, a truncated hartley series together withthe operational matrix of integration and integration of the crossproduct of two cas vectors are used for finding the solution ofvariational problems. two illustrative examples are included todemon...

A new algorithm for the approximation and simulation of twofold iterated stochastic integrals together with corresponding Lévy areas driven by a multidimensional Brownian motion is proposed. The based on truncated Fourier series approach. However, remainder terms differs from approach considered Wiktorsson (2001). As main advantage, presented makes use diagonal covariance matrix one part term h...