一类微分算子谱函数的渐近性
The asymptotical behavior of spectral function of one family of differential operators
摘要：
研究了一类定义在位势空间$L_2[0,+\infty)$中的二阶自伴微分算子的谱函数$ρ(λ, ε),ε> 0$的渐近性态，其中位势依赖于$ε$ .给出了负$λ$的谱函数导数的估计，并证明了$ρ'(λ, ε)$到$ρ'(λ, 0)$与$ε\to +0$的弱收敛性.
英文摘要：
Is considered the asymptotical behavior of spectral function $ρ(λ, ε),ε> 0$, of one family of self adjoint differential operators of second order, defined in space $L_2[0,+\infty)$ with potentials, depending on $ε$. Are given evaluations for the derivative of spectral function for negative $λ$ and is proved the weak convergence of $ρ'(λ, ε)$ to $ρ'(λ, 0)$ with $ε\to +0$.
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