论文标题
关于第四阶差分操作员方程的扩展和光谱问题
On extensions and spectral problems for fourth order differential operator equation
论文作者
论文摘要
本文的目的首先是根据最小和最大运算符的边界条件以及与四阶差分操作员方程相关的最小运算符的自我关节扩展来研究定义域。此外，我们为该操作员提供了必要和充分的条件，使其具有纯粹的离散或连续频谱，可以从$σ_P分解的情况下扩展，如果纯离散频谱，$σ_P，$研究渐近谱。最后，提供新的，更通用的方法，以评估与一个类边界价值问题相关的离散频谱的运算符的正则轨迹。
The aim of the paper is firstly to study domains of definitions in terms of boundary conditions of minimal and maximal operators, as well as selfadjoint extensions of a minimal operator associated with the fourth-order differential operator equation. Further, we give necessary and sufficient conditions for that operators to have a purely discrete or continuous spectrum, to exist extension with resolvent from $σ_p,$ study asymptotics of spectrum in case pure discrete spectrum. Finally, give the new and more general method for evaluations of regularized traces of operators with discrete spectrum associated with one class boundary value problems.
