Geodesic
Expansion in characteristic functions of the Schrödinger operator with a singular potential
Matematičeskie zametki, Tome 15 (1974) no. 3, pp. 455-465 
G. N. Gestrin. Expansion in characteristic functions of the Schrödinger operator with a singular potential. Matematičeskie zametki, Tome 15 (1974) no. 3, pp. 455-465. http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a12/
@article{MZM_1974_15_3_a12,
     author = {G. N. Gestrin},
     title = {Expansion in characteristic functions of the {Schr\"odinger} operator with a~singular potential},
     journal = {Matemati\v{c}eskie zametki},
     pages = {455--465},
     year = {1974},
     volume = {15},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a12/}
}
TY  - JOUR
AU  - G. N. Gestrin
TI  - Expansion in characteristic functions of the Schrödinger operator with a singular potential
JO  - Matematičeskie zametki
PY  - 1974
SP  - 455
EP  - 465
VL  - 15
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a12/
LA  - ru
ID  - MZM_1974_15_3_a12
ER  - 
%0 Journal Article
%A G. N. Gestrin
%T Expansion in characteristic functions of the Schrödinger operator with a singular potential
%J Matematičeskie zametki
%D 1974
%P 455-465
%V 15
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a12/
%G ru
%F MZM_1974_15_3_a12

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the spectral function of the operator $-\Delta+v(x)$ in three-dimensional space, where $v(x)$ is measurable and belongs to $L_2$. We study the differentiability of this function with respect to some measure. Simultaneously, we give estimates of the characteristic functions of a continuous spectrum at infinity. This justifies the decomposition of an arbitrary function in terms of the characteristic functions of an operator with this type of potential.