Self-adjointness of unbounded tridiagonal operators and spectra of their finite truncations

This paper addresses two different but related questions regarding an unbounded symmetric tridiagonal operator: its self-adjointness and the approximation of its spectrum by the eigenvalues of its finite truncations. The sufficient conditions given in both cases improve and generalize previously known results. It turns out that, not only self-adjointness helps to study limit points of eigenvalues of truncated operators, but the analysis of such limit points is a key help to prove self-adjointness. Several examples show the advantages of these new results compared with previous ones. Besides, an application to the theory of continued fractions is pointed out.     

Muckenhoupt weights with singularities on closed lower dimensional sets in spaces of homogeneous type

We give sufficient conditions on a real number β and on a closed set F   in a general space of homogeneous type (X,d,μ)$(X,d,\mu )$ in such a way that μ(B(x,d(x,F)))^β$\mu {(B(x,d(x,F)))}^{\beta }$ becomes a Muckenhoupt weight. In order to prove our result, we modify the underlying space so that it becomes 1-Ahlfors regular.     

A necessary and sufficient condition for Hardy's operator in

The equivalent conditions are proved for the Hardy inequality to be fulfilled in the norms of a Lebesgue space with variable exponent . It is assumed that the function is monotone and positive on (0, 1).     

Isometries on and monotone functions

We study necessary and sufficient conditions on a bounded operator T defined on the Hilbert space to be an isometry and show that, under suitable hypotheses, it suffices to restrict T to a smaller class of functions (e.g., if , to the cone of positive and decreasing functions). We also consider the problem of characterizing the sets for which the orthogonal projection of the operator T on is also an isometry. Finally, we illustrate our results with several examples involving classical operators on different settings.     

A separation theorem for the weak s-convex orders

The present paper extends to higher degrees the well-known separation theorem decomposing a shift in the increasing convex order into a combination of a shift in the usual stochastic order followed by another shift in the convex order. An application in decision making under risk is provided to illustrate the interest of the result.     

EXISTENCE OF POSITIVE MULTIPLE SOLUTIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN OPERATOR

In this paper, we consider a two-point fractional boundary value problem. We provide sufficient conditions for the existence of multiple positive solutions to the boundary value problem by Krasnosel＇skii fixed point theorem on the cone.     

分层变分包含问题中经由分层不动点途径的黏性方法

基于一原创技术—指标选取法,以黏性法分层逼近可数族非线性映射之公共不动点.并于适当条件下得一强收敛定理,用以解决Hilbert空间背景下之分层变分包含问题.     

Rough singular integrals associated with surfaces of Van der Corput type简

In this paper,the authors establish the Lp-mapping properties for a class of singular integrals along surfaces in Rn of the form {φ(|u|)u : u ∈ Rn} as well as the related maximal operators provided that the function φ satisfies certain oscillatory integral estimates of Van der Corput type,and the integral kernels are given by the radial function h ∈Δγ(R+) for γ 1 and the sphere function Ω∈ Fβ(Sn.1) for some β 0,which is distinct from H1(Sn.1).     

二维区间密度加权算子及其应用

针对不确定多属性决策中的属性信息分布不均匀,且评价信息多数为二维信息的情况,本文提出了二维区间密度加权算子(TDIDW算子)的属性信息集结方法.依据密度算子的集结过程特点,文章首先定义了二维区间密度加权算子及其合成算子,然后介绍了基于灰色区间聚类法的评价信息分组方法以及基于非线性模型的密度加权向量确定方法,最后进行了算例验证.验证结果表明,该方法可以有效地解决由于属性信息分布不均匀而导致评价结果不准确的问题.     

Approximation of inverse operators by a new family of high‐order iterative methods

The main goal of this paper is to approximate inverse operators by high‐order Newton‐type methods with the important feature of not using inverse operators. We analyse the semilocal convergence, the speed of convergence, and the efficiency of these methods. We determine that Chebyshev's method is the most efficient method and test it on two problems: one associated to the heat equation and the other one to a boundary value problem. We consider examples with matrices that are close to be singular and/or are badly conditioned. We check the robustness and the stability of the methods by considering situations with many steps and noised data. Copyright © 2013 John Wiley & Sons, Ltd.