The asymptotical behavior of spectral function of one family of differential operators

Abstract

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 $ε\to +0$.