Geodesic
Expansion in characteristic functions of the Schr\"odinger operator with a~singular potential
Matematičeskie zametki, Tome 15 (1974) no. 3, pp. 455-465.

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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. 
@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},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a12/}
}
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G. N. Gestrin. Expansion in characteristic functions of the Schr\"odinger 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/