POINTWISE CONVERGENCE FOR EXPANSIONS IN SPHERICAL MONOGENICS

We offer a new approach to deal with the pointwise convergence of FourierLaplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Riemann operator, we obtain the spherical monogenic expansions of square integrable functions on the unit sphere. Based on the generalization of Fueter＇s theorem inducing monogenic functions from holomorphic functions in the complex plane and the classical Carleson＇s theorem, a pointwise convergence theorem on the new expansion is proved. The result is a generalization of Carleson＇s theorem to the higher dimensional Euclidean spaces. The approach is simpler than those by using special functions, which may have the advantage to induce the singular integral approach for pointwise convergence problems on the spheres.     

Pointwise characterization for combinations of Szász-Mirakjan operators

The purpose of this paper is to characterize the pointwise rate of convergence for the combinations of Szász-Mirakjan operators using Ditzian-Totik modulus of smoothness.     

Hermite插值多项式的导数逼近函数的导数

给出基于混合型Jacobi气点的Hermite插值多项式的导数和函数的县数之间的偏差的点态估计．     

Local Convergence of the Symmetric Rank-One Iteration

We consider conditions under which the SR1 iteration is locally convergent. We apply the result to a pointwise structured SR1 method that has been used in optimal control.     

加权再生核空间中信号的平均采样与重构

主要讨论L_v~p的加权再生核子空间中信号的平均采样与重构.首先,针对两种平均采样泛函建立了采样稳定性;其次,基于概率测度给出一个一般的迭代算法,将迭代逼近投影算法和迭代标架算法统一起来;最后,针对被白噪声污染的平均样本给出了信号重构的渐进点态误差估计.     

Spaces of Densely Continuous Forms

The set C(X,Y) of continuous functions from a topological space X into a topological space Y is extended to the set D(X,Y) of densely continuous forms from X to Y, such form being a kind of multifunction from X to Y. The topologies of pointwise convergence, uniform convergence, and uniform convergence on compact sets are defined for D(X,Y), for locally compact spaces X and metric spaces Y having a metric satisfying the Heine–Borel property. Under these assumptions, D(X,Y) with the uniform topology is shown to be completely metrizable. In addition, if X is compact, D(X,Y) is completely metrizable under the topology of uniform convergence on compact sets. For this latter topology, an Ascoli theorem is established giving necessary and sufficient conditions for a subset of D(X,Y) to be compact.     

Pointwise convergence along a tangential curve for the fractional Schrödinger equation with 0 < m < 1

In this article, we study the pointwise convergence problem about solution to the fractional Schrödinger equation with 0 < m < 1 along a tangential curve and estimate the capacitary dimension of the divergence set. We extend the results of Cho and Shiraki (2021) for the case m > 1 to the case 0 < m < 1, which is sharp up to the endpoint.     

A conservative difference scheme with optimal pointwise error estimates for two-dimensional space fractional nonlinear Schrödinger equations

In this paper, a linearized semi-implicit finite difference scheme is proposed for solving the two-dimensional (2D) space fractional nonlinear Schrödinger equation (SFNSE). The scheme has the property of mass and energy conservation at the discrete level, with an unconditional stability and a second-order accuracy for both time and spatial variables. The main contribution of this paper is an optimal pointwise error estimate for the 2D SFNSE, which is rigorously established for the first time. Moreover, a novel technique is proposed for dealing with the nonlinear term in the equation, which plays an essential role in the error estimation. Finally, the numerical results confirm well with the theoretical findings.     

Pointwise error estimates of the bilinear SDFEM on Shishkin meshes

A model singularly perturbed convection–diffusion problem in two space dimensions is considered. The problem is solved by a streamline diffusion finite element method (SDFEM) that uses piecewise bilinear finite elements on a Shishkin mesh. We prove that the method is convergent, independently of the diffusion parameter ε, with a pointwise accuracy of almost order 11/8 outside and inside the boundary layers. Numerical experiments support these theoretical results. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Pointwise estimate of solutions of isentropic Navier-Stokes equations in even space-dimensions

This paper is concerned with the dissipation of solutions of the isentropic Navier-Stokes equations in even and bigger than two multi-dimensions. Pointwise estimates of the time-asymptotic shape of the solutions are obtained and the generalized Huygan's principle is exhibited. The approch of the paper is based on the detailed analysis of the Green function of linearized system. This is used to study the coupling of nonlinear diffusion waves.