Positivity of Fock Toeplitz Operators via the Berezin Transform

This paper deals with the relationship between the positivity of the Fock Toeplitz operators and their Berezin transforms. The author considers the special case of the bounded radial function φ(z) = a + be~(-α|z|~2)+ ce~(-β|z|~2), where a, b, c are real numbers and α, β are positive numbers. For this type of φ, one can choose these parameters such that the Berezin transform of φ is a nonnegative function on the complex plane, but the corresponding Toeplitz operator Tφ is not positive on the Fock space.     

Analytical Hartree–Fock wave functions for the atoms Cs to Lr

 Analytical approximations to Hartree–Fock wave functions are constructed using Slater-type functions for the ground states of all 49 neutral atoms from Cs (Z=55) to Lr (Z=103). The current compilation is more extensive and more accurate than previous ones. The wave functions are available upon request from the authors or from the Web page http://www.unb.ca/chem/ajit/download.htm on the Internet. Received: 6 December 1999 / Accepted: 29 February 2000 / Published online: 12 May 2000     

与闪电过程有关的NII离子能级寿命的理论计算

用相对论多组态DiracFock方法,系统地计算了与闪电过程有关的NII离子2p2,2s2p3,2p3s,2p3p,2p3d组态能级之间的辐射跃迁概率,并由此推算出这些组态的35个能级的寿命.计算中考虑了相对论效应、电子关联、延迟效应等重要贡献.与已有的理论计算比较,目前计算的结果更接近最新实验值.据此,进一步给出了2p3d3F能级寿命新的理论预言值     

Electronic Fock space as associative superalgebra

A new algebraic structure on a finite dimensional electronic Fock space is studied in detail. This structure is defined in terms of a certain multiplication of many electron wave functions and has close interrelation with coupled cluster and similar approaches. Its study simplifies the mathematical backgrounds of these approaches. Even more, it leads to relations that would be very difficult to derive using conventional technique. Formulas for action of the creation‐annihilation operators on products of state vectors are derived. Explicit expressions for action of simplest particle‐conserving products of the creation‐annihilation operators on powers of state vectors are given. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

解析Sobolev型空间上的算子与算子代数

介绍Hardy-Sobolev空间和Fock空间及其算子与算子代数研究方面所做的工作,包括对这两类空间上几类特殊算子有界性、紧性、Fredholm性、指标理论、谱和本性谱、范数和本性范数、Schatten-p类的讨论,以及由它们所生成的C~*-代数的研究.     

Leibniz algebras associated with representations of filiform Lie algebras

In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra $n_{n,1}$. We introduce a Fock module for the algebra $n_{n,1}$ and provide classification of Leibniz algebras $L$ whose corresponding Lie algebra $L/I$ is the algebra $n_{n,1}$ with condition that the ideal $I$ is a Fock $n_{n,1}$-module, where $I$ is the ideal generated by squares of elements from $L$.We also consider Leibniz algebras with corresponding Lie algebra $n_{n,1}$ and such that the action $I\times n_{n,1}\to I$ gives rise to a minimal faithful representation of $n_{n,1}$. The classification up to isomorphism of such Leibniz algebras is given for the case of $n=4$.     

A class of Gaussian processes with fractional spectral measures

We study a family of stationary increment Gaussian processes, indexed by time. These processes are determined by certain measures σ (generalized spectral measures), and our focus here is on the case when the measure σ is a singular measure. We characterize the processes arising from σ when σ is in one of the classes of affine selfsimilar measures. Our analysis makes use of Kondratiev white noise spaces. With the use of a priori estimates and the Wick calculus, we extend and sharpen (see Theorem 7.1) earlier computations of Ito stochastic integration developed for the special case of stationary increment processes having absolutely continuous measures. We further obtain an associated Ito formula (see Theorem 8.1).     

Orlicz Figà – Talamanca Herz algebras and invariant means

The aim of this paper is to initiate a systematic study of the Orlicz Figà – Talamanca Herz algebras on locally compact groups. We also introduce and study invariant means on the dual of these algebras.