Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 28, Tome 270 (2000), pp. 336-349
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M. M. Faddeev; R. G. Shterenberg. On the similarity of some singular differential operators to selfadjoint ones. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 28, Tome 270 (2000), pp. 336-349. http://geodesic.mathdoc.fr/item/ZNSL_2000_270_a17/
@article{ZNSL_2000_270_a17,
author = {M. M. Faddeev and R. G. Shterenberg},
title = {On the similarity of some singular differential operators to selfadjoint ones},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {336--349},
year = {2000},
volume = {270},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_270_a17/}
}
TY - JOUR
AU - M. M. Faddeev
AU - R. G. Shterenberg
TI - On the similarity of some singular differential operators to selfadjoint ones
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2000
SP - 336
EP - 349
VL - 270
UR - http://geodesic.mathdoc.fr/item/ZNSL_2000_270_a17/
LA - ru
ID - ZNSL_2000_270_a17
ER -
%0 Journal Article
%A M. M. Faddeev
%A R. G. Shterenberg
%T On the similarity of some singular differential operators to selfadjoint ones
%J Zapiski Nauchnykh Seminarov POMI
%D 2000
%P 336-349
%V 270
%U http://geodesic.mathdoc.fr/item/ZNSL_2000_270_a17/
%G ru
%F ZNSL_2000_270_a17
The singular differential operator $Lf(x)=-\operatorname{sign}x\frac{d^2f(x)}{dx^2}+p(x)f(x)$ is studied. It is proved that if the second moment of $p$ is finite and $L$ has no nonreal eigenvalues, then $L$ is similar to a selfadjoint operator. The proof is based upon an integral resolvent criterion for the similarity applied to a wide class of functions $p(x)$.
