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,+∞)
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→+0
.