Chaotic weighted shifts in Bargmann space

This paper deals with the unilateral backward shift operator T on a Bargmann space F(C). This space can be identified with the sequence space ?²(N). We use the hypercyclicity criterion of Bès, Chan, and Seubert and the program of K.-G. Grosse-Erdmann to give a necessary and sufficient condition in order that T be a chaotic operator. The chaoticity of differentiation which correspond to the annihilation operator in quantum radiation field theory is in view, since the Bargmann space is an infinite-dimensional separable complex Hilbert space.     

一类向量值积分方程的优化问题

提出了一类带有参数的向量值积分的优化问题,将H ardy空间中的一些概念推广到了局部凸空部间,尤其是将H ankel算子、最小模型匹配误差、最优解等概念推广到了局部凸空间.     

套代数模中酉算子的存在性

假设套N是可接受的,则得到弱闭Alg(N)-模u中存在酉算子的充要条件是I-=I且对任意 M>0,有N->0.     

Homogenization of Semilinear Parabolic Operators in a Perforated Cylinder

In this paper, we consider a semilinear parabolic equation of second order with lower term a power function of the unknown function and prove that the sequence of solutions in a perforated cylinder tends to a solution in a unperforated cylinder if the radii of rejected balls in the parabolic metric tend to zero at the rate depending on the exponent of the power function in the lower term.     

超球Bloch空间上的有界加权复合算子

本文证明了高维超球Bloch空间上的加权复合算子成为有界算子的一个充分且必要的条件.     

On unbounded subnormal operators

A minimal normal extension of unbounded subnormal operators is established and characterized and spectral inclusion theorem is proved. An inverse Cayley transform is constructed to obtain a closed unbounded subnormal operator from a bounded one. Two classes of unbounded subnormals viz analytic Toeplitz operators and Bergman operators are exhibited.     

Quasi-compactness and absolutely continuous kernels

We show how the essential spectral radius r _e (Q) of a bounded positive kernel Q, acting on bounded functions, is linked to the lower approximation of Q by certain absolutely continuous kernels. The standart Doeblin’s condition can be interpreted in this context, and, when suitably reformulated, it leads to a formula for r _e (Q). This results may be used to characterize the Markov kernels having a quasi-compact action on a space of measurable functions bounded with respect to some test function, when no irreducibilty and aperiodicity are assumed.      

Hardy空间上Fourier级数的Cesàro求和

研究了Hardy空间上Ces劋ro算子的有界性.证明极大Ces劋ro算子的强型和弱型有界估计.其弱有界性估计是精确的.推广和加强了已有研究结果.     

Symmetric Functionals and Singular Traces

We study the construction and properties of positive linear functionals on symmetric spaces of measurable functions which are monotone with respect to submajorization. The construction of such functionals may be lifted to yield the existence of singular traces on certain non-commutative Marcinkiewicz spaces which generalize the notion of Dixmier trace.     

两点边值问题解的存在性

本文讨论两点边值问题解的存在性,在没有孤立性条件下,获得了不动点定理,作为应用实例,给出了反应扩散方程稳态解的存在性证明。