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

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

1997-02-12

arxiv.org/abs/funct-an/9702012v1

Mathematics

Functional Analysis

5 pages, AMSTeX, to appear in Proceedings of the Seventh Crimean Autumn Mathematical School-Simposium on Spectral and Evolutio

Scientific paper

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 $\epsilon \to +0$.

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