具有Lenard递推结构之发展方程族的Lax表示

该文对具有Ｌｅｎａｒｄ递推结构的发展方程族，通过转换速推结构为一个算子方程给出了Ｌａｘ表示的一种理论描述．这种描述可应用于各种１＋１维可积系统族Ｌａｘ表示的寻求之中，本文仅就ＫｄＶ可积族和Ａｎｔｏｎｏｗｉｃｚ—Ｆｏｒｄｙ可积族详细阐述了Ｌａｘ表示的具体构造过程．

TO族零曲率表示的统一结构

可积族零曲率表示的统一结构已被提出,但对已知的可积族(除文[1]讨论的耦合Kdv族外)还未见给出相应的结果。本文对TD可积族得到了相应特征算子方程的一个解及初始非等谱向量场,生成了等谱与非等谱TD可积族的二族Lax算子。

On Feasibility of Variable Separation Method Based on Hamiltonian System for a Class of Plate Bending Equations

The eigenfunction system of infinite-dimensional Hamiltonian operators appearing in the bending problem of rectangular plate with two opposites simply supported is studied. At first, the completeness of the extended eigenfunction system in the sense of Cauchy＇s principal value is proved. Then the incompleteness of the extended eigenfunction system in general sense is proved. So the completeness of the symplectic orthogonal system of the infinite-dimensional Hamiltonian operator of this kind of plate bending equation is proved. At last the general solution of the infinite dimensional Hamiltonian system is equivalent to the solution function system series expansion, so it gives to theoretical basis of the methods of separation of variables based on Hamiltonian system for this kind of equations.

Toeplitz operators on H^2(iR)

In this paper,the essential spectra of Toeplitz operators is discussed,and the K-theory of the Toeplitz algebra generated by {Tφ|φ∈C(iR)} is computed.In addition,the characteristic equation of Toeplitz operators is obtained and the algebraic properties of Toeplitz operators are discussed.

Continuous Spectrum Measure of a Class of Schrdinger Operators

We consider the discrete Schrdinger operator acting on l 2(Z) with the potential V n, the sequence consisting of k+1 symbols: {0,1,2,…,k}, and prove that it exhibits purely continuous spectrum.