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

Abstract

Is considered the asymptotical behavior of spectral function $\rho(\lambda, \epsilon),\epsilon > 0$, of one family of self adjoint differential operators of second order, defined in space $L_2[0,+\infty)$ with potentials, depending on $\epsilon$. Are given evaluations for the derivative of spectral function for negative $\lambda$ and is proved the weak convergence of $\rho'(\lambda, \epsilon)$ to $\rho'(\lambda, 0)$ with $\epsilon \to +0$.