A Gleason–Kahane–Żelazko theorem for the Dirichlet space

We show that every linear functional on the Dirichlet space that is non-zero on nowhere-vanishing functions is necessarily a multiple of a point evaluation. Continuity of the functional is not assumed. As an application, we obtain a characterization of weighted composition operators on the Dirichlet space as being exactly those linear maps that send nowhere-vanishing functions to nowhere-vanishing functions.We also investigate possible extensions to weighted Dirichlet spaces with superharmonic weights. As part of our investigation, we are led to determine which of these spaces contain functions that map the unit disk onto the whole complex plane.     

Cn中不同域的复合算子

令Ω1与Ω2与C^n中的两个有界齐性域，假设φ：1Ω→Ω2是一个全纯映射。在本中，我们研究相应的复合算子Cφ：β（Ω2）→β（Ω1）的有界性和紧性，特别地，我们讨论取B^n和U^n的情形。     

Generalized Variation of Mappings with Applications to Composition Operators and Multifunctions

We study (set-valued) mappings of bounded -variation defined on the compact interval I and taking values in metric or normed linear spaces X. We prove a new structural theorem for these mappings and extend Medvedev's criterion from real valued functions onto mappings with values in a reflexive Banach space, which permits us to establish an explicit integral formula for the -variation of a metric space valued mapping. We show that the linear span GV (I;X) of the set of all mappings of bounded -variation is automatically a Banach algebra provided X is a Banach algebra. If h:I× X Y is a given mapping and the composition operator is defined by (f)(t)=h(t,f(t)), where tI and f:I X, we show that :GV (I;X) GV (I;Y) is Lipschitzian if and only if h(t,x)=h₀(t)+h₁(t)x, tI, xX. This result is further extended to multivalued composition operators with values compact convex sets. We prove that any (not necessarily convex valued) multifunction of bounded -variation with respect to the Hausdorff metric, whose graph is compact, admits regular selections of bounded -variation.     

单位球上Dp到βμ的加权复合算子

讨论了单位球上D打ichlet型空间砩到μ-Bloch空间艮的加权复合算子的有界性和紧性问题,并给出了 Tψ,φ为有界算子和紧算子的充要条件．     

Some properties of Stepanov-like almost automorphic functions and applications to abstract evolution equations

This article is concerned with some properties of Stepanov-like almost automorphic (S ^p -a.a.) functions. We establish a composition theorem about S ^p -a.a. functions, and with its help, study the existence and uniqueness of almost automorphic solutions for semilinear evolution equations in Banach spaces. Moreover, integration and differentiation of S ^p -a.a. functions are discussed. Some theorems extend earlier results.     

Réflexivité d’une extension d’un opérateur normal par un opérateur nilpotent

Let T be an extension of a one to one normal operator A by a nilpotent operator N. In this paper we calculate the defect of reflexivity of T. We give a necessary and sufficient condition to insure the reflexivity of such extensions. In particular, it is shown that T is reflexive when N is reflexive.     

饲喂频率对鲈鱼生长及体生化成分的影响

选取同一种饵料设置1次·d-1、2次·d-1、3次·d-1、4次·d-14个饲喂频率,采用静水连续充气养殖系统,在盐度为26.0%～27.0%、温度为26～30℃条件下对鲈鱼(85.95±2.04)g进行为期40d的生长实验.结果表明:(1)饲喂频率影响鲈鱼的生长是由食物转化率和摄食率的提高共同引起的.(2)水分含量随饲喂频率的增高而保持不变;蛋白质含量随饲喂频率的增加,基本保持不变;脂肪含量随饲喂频率的增高而明显减少;灰分含量随饲喂频率的增多而明显增加.(3)鲈鱼的适宜饲喂频率为2次·d-1.     

On the Existence Of Consistent Price Systems

We formulate a sufficient condition for the existence of a consistent price system (CPS), which is weaker than the conditional full support condition (CFS). We use the new condition to show the existence of CPSs for certain processes that fail to have the CFS property. In particular this condition gives sufficient conditions, under which a continuous function of a process with CFS admits a CPS, while the CFS property might be lost.