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。     

Geometric phase as a simple closed-form integral

For a general evolution of a quantal system, the geometric phase measured with reference to a given initial state is derived as an integral of a function of the pure state density operator by invoking the Pancharatnam connection continuously.     

A Construction of Multiresolution Analysis on Interval

We present a concrete method of constructing multiresolution analysis on interval. The method generalizes the corresponding results of Cohen, Daubechies and Vial [Appl. Comput. Harmonic Anal., 1（1993）, 54-81]. By the use of the subdivision operator, the expressions of the constructed functions are more compact. Furthermore, the method reveals more clearly some properties of multiresolution analysis with certain approximation order.     

Supersonic and intersonic cracking in rock-like material under remote stresses

There are many models that attempt to describe the dynamics of seismology that include plasticity, temperature effect, dissipation and viscosity. While these details are important, useful results of dynamic deformation can be obtained from simple models. The essential features are the internal geometry of porosity and cracked medium. They involve the specific surface or the average distance between one crack to another. This entails the internal sizes of micro- and mesostructure that are not considered by classical mechanics. Only one new parameter is introduced in the simple model, the specific surface while the other parameters are the Lame constants and density.     

Heat Content Asymptotics for Oblique Boundary Conditions

We consider the short-time heat content asymptotics for oblique boundary conditions. The first few coefficients in the asymptotic expansion are calculated.     

齐型空间上的加权Herz空间的分解及其应用

定义了一类齐型空间上的加权Herz空间，研究了它的分解特征，并利用此特征研究了定义在这些空间上的一类次线性算子的有界性。