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 ${\rho }^{\prime }(\lambda ,\epsilon )$ to ${\rho }^{\prime }(\lambda ,0)$ with $\epsilon \to +0$.

arXiv comment5 pages, AMSTeX, to appear in Proceedings of the Seventh Crimean Autumn Mathematical School-Simposium on Spectral and Evolutionary Problems (September, 18-29, 1996, Sevastopol, Ukraine)

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