Given the Sturm-Liouville eigenfunction expansion of an ¿2 function fix), summability theory provides means for recovering the value of fix¿) at points x0 where / is sufficiently regular. If the coefficients in the expansion are perturbed slightly (in the I^ norm), a stable summation method will recover from the perturbed expansion a good approximation to fix¿). In this paper we develop stable ...

After the successful applications of the combination of the method of fundamental solutions (MFS), the method of particular solutions (MPS), and the eigenfunctions expansion method (EEM) to solve 2D homogeneous and nonhomogeneous diffusion equations by Young et al. (Young et al., Numer Meth Part Differ Equat 22 (2006), 1173), this article intends to extend the same fundamental concepts to calcu...

We introduce a new method for computing the Hubert transform on the real line. It is a collocation method, based on an expansion in rational eigenfunctions of the Hubert transform operator, and implemented through the Fast Fourier Transform. An error analysis is given, and convergence rates for some simple classes of functions are established. Numerical tests indicate that the method compares f...

Abstract In this work, we consider a boundary value problem for q -Dirac equation. We prove orthogonality of the eigenfunctions, realness eigenvalues, and study asymptotic formulas eigenfunctions. show that eigenfunctions form complete system, obtain expansion formula with respect to derive Parseval’s equality. construct Weyl solution function. uniqueness theorem inverse

Abstract We investigate how the derivative expansion in HAL QCD method works to extract physical observables, using a separable potential quantum mechanics, which is solvable but highly non-local coordinate system. consider three cases for inputs determine expansion: (1) energy eigenfunctions, (2) time-dependent wave functions as solutions Schrödinger equation with some boundary conditions, and...

A previous fully relativistic time-dependent close-coupling method [Phys. Rev. A 81, 063431 (2010)], developed to study the photoionization of highly charged atomic ions, is substantially modified to include the full electromagnetic-field potential. Expansion of a one active electron wave function for the time-dependent Dirac equation in spin-orbit eigenfunctions yields close-coupled equations ...

The properties of the Karhunen-Lo&e (KL) expansion of the derivative u,(x) of an inhomogeneous random process possessing viscous boundary-layer behavior are studied in relation to questions of efficient representation for numerical Galerkan schemes for computational simulation of turbulence. Eigenfunctions and eigenvalue spectra are calculated for the randomly forced one-dimensional Burgers’ mo...

In this paper we will consider a new scheme of image database retrieval by fast Hermite projection method. The database contained 4100 images. The method is based on an expansion into series of eigenfunctions of the Fourier transform. Photo normalization includes following steps of preprocessing: resampling, corners detection, rotation, perspective and parallelogram elimination, painting cuttin...

We study the division of components of energy eigenfunctions, as the expansion of perturbed states in unperturbed states, into nonperturbative and perturbative parts in a three-orbital schematic shell model possessing a chaotic classical limit, the Hamiltonian of which is composed of a Hamiltonian of noninteracting particles and a perturbation. The perturbative parts of eigenfunctions are expan...

We derive the biorthogonality condition for axisymmetric Stokes flow in a region between two concentric spheres. This biorthogonality condition is a property satisfied by the eigenfunctions and adjoint eigenfunctions, which is needed to compute the coefficients of the eigenfunction expansion solution of the corresponding creeping flow problem.