THE ISOMETRIC EXTENSION OF AN INTO MAPPING FROM THE UNIT SPHERE S[e（Γ）] TO THE UNIT SPHERE S（E）

This is such a article to consider an ＂into＂ isometric mapping between two unit spheres of two infinite dimensional spaces of different types. In this article, we find a useful condition （using the Krein-Milman property） under which an into-isometric mapping from the unit sphere of e（Γ） to the unit sphere of a normed space E can be linearly isometric extended.     

Fourier series of half-range functions by smooth extension

This paper considers Fourier series approximations of one- and two-dimensional functions over the half-range, that is, over the sub-interval [0, L] of the interval [−L, L] in one-dimensional problems and over the sub-domain [0, L_x] × [0, L_y] of the domain [−L_x, L_x] × [−L_y, L_y] in two-dimensional problems. It is shown how to represent these functions using a Fourier series that employs a smooth extension. The purpose of the smooth extension is to improve the convergence characteristics otherwise obtained using the even and odd extensions. Significantly improved convergence characteristics are illustrated in one-dimensional and two-dimensional problems.     

具有预防性维修策略的可修复系统的指数稳定性

利用算子半群理论研究了具有预防性维修策略的可修复系统,通过分析系统算子的谱分布,以及系统算子生成C0半群{T(t)}的本质谱增长阶,证明了C0半群{T(t)}是拟紧半群.同时也证明了该半群还是不可约的.进而得到了可修复可用度的指数稳定性.     

On Extension of 1-Lipschitz Mappings between Two Unit Spheres of lp(Γ) Type Spaces (1

FANG Xi Nian 《数学研究与评论》2009,29(4)

Nonvanishing at spatial extremity solutions of the defocusing nonlinear Schrödinger equation

We show local existence of certain type of solutions for the Cauchy problem of the defocusing nonlinear Schrödinger equation with pure power nonlinearity, in various cases of open sets, unbounded or bounded. These solutions do not vanish at the boundary or at infinity. We also show, in certain cases, that these solutions are unique and global.     

Automorphisms of Extensions of ℚ by a Direct Sum of Finitely Many Copies of ℚ

Let G be an extension of ℚ by a direct sum of r copies of ℚ. (1) If G is abelian, then G is a direct sum of r + 1 copies of ℚ and AutG ≅ GL(r + 1, Q); (2) If G is non-abelian, then G is a direct product of an extraspecial ℚ-group E and m copies of ℚ, where E/ζE is a linear space over Q with dimension 2n and m + 2n = r. Furthermore, let AutG′G be the normal subgroup of AutG consisting of all elements of AutG which act trivially on the derived subgroup G′ of G, and AutG/ζG,ζGG be the normal subgroup of AutG consisting of all central automorphisms of G which also act trivially on the center ζG of G. Then (i) The extension 1 → AutG′G → AutG → AutG′ → 1 is split; (ii) AutG′G/AutG/ζG,ζGG ≅ Sp(2n,Q) × (GL(m, Q) ⋉ ℚ(m)); (iii) AutG/ζG,ζGG/InnG ≅ ℚ(2nm).     

Isometric Extension Problem Between Strictly Convex Two-dimensional Normed Spaces

In this paper, based on the smooth point of the unit ball and its support linear functional,we show two equivalent formulations of the isometric extension problem between the unit spheres of strictly convex two-dimensional normed spaces. We prove that these equivalent formulations have a positive answer in a special case.     

加权Begman空间的加权复合算子的本性模

利用上极限,给出了单位球上加权Bergman空间的加权复合算子的本性模的表示．     

Linear fractional composition operators on the Dirichlet space in the unit ball

We investigate the adjoints of linear fractional composition operators Cφ acting on classical Dirichlet space D(BN ) in the unit ball BN of CN , and characterize the normality and essential normality of Cφ on D(BN ) and the Dirichlet space modulo constant function D0(BN ), where φ is a linear fractional map of BN . In addition, we also show that for any non-elliptic linear fractional map φ of BN , the composition maps σ ο φ and φ ο σ are elliptic or parabolic linear fractional maps of BN .     

Weighted differentiation composition operator from logarithmic Bloch spaces to Bloch‐type spaces

In this paper, we give a new characterization for the boundedness of weighted differentiation composition operator from logarithmic Bloch spaces to Bloch‐type spaces and calculate its essential norm in terms of the n‐th power of induced analytic self‐map on the unit disk. From which a sufficient and necessary condition of compactness of this operator follows immediately.