Error estimate of Fourier pseudo-spectral method for multidimensional nonlinear complex fractional Ginzburg–Landau equations

In this paper, we discuss the error estimate of Fourier pseudo-spectral method for multidimensional nonlinear complex space fractional Ginzburg-Landau equations. The continuous mass and energy inequalities as well as their discrete versions are presented. Moreover, by the discrete mass and energy inequalities, the error estimate of the Fourier pseudo-spectral scheme is established, and the scheme is proved to have the spectral accuracy.     

Reconstruction of Splines from Nonuniform Samples

In this paper, we study the reconstruction of spline functions from their nonuniform samples. We investigate the existence and uniqueness of the solution of the following problem: for given data {(x_n, y_n) : n ∈ Z}, find a cardinal spline f(x), of a given degree, satisfying yn = f(x_n), n ∈ Z.Several necessary and/or sufficient conditions for the existence and uniqueness of the solution of the problem are derived. Finally, an example and some applications are presented to illustrate the main results.     

The density theorem for discrete series representations restricted to lattices

This article considers the relation between the spanning properties of lattice orbits of discrete series representations and the associated lattice co-volume. The focus is on the density theorem, which provides a trichotomy characterizing the existence of cyclic vectors and separating vectors, and frames and Riesz sequences. We provide an elementary exposition of the density theorem, that is based solely on basic tools from harmonic analysis, representation theory, and frame theory, and put the results into context by means of examples.     

基于点线插值的离散最小二乘后处理方法

构造了一种基于点线插值有限元的后处理方法,这种后处理方法具有好的超收敛性和最小二乘的稳定性.     

Maximal Estimates of Schrödinger Equations on Rearrangement Invariant Sobolev Spaces

We establish the maximal estimates for the solutions of some initial value problems on rearrangement-invariant quasi-Banach function spaces. Our result covers the cases for which the initial value problem is given by the Schrödinger equation.