Geodesic
Schr\"odinger Operators with Singular Potentials
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 262-271

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Schrödinger operators are investigated whose potentials represent generalized functions. A problem of physically correct determination of such operators is solved by two different methods in the case of one and several variables. In the first case, the potential must represent an element of the negative space $W^{-1}_2$; then, the operator obtained can be analyzed in greater detail. In the second case, a requirement is imposed on the potential that it must belong to the class of multipliers from $W^{1}_2$ to $W^{-1}_2$. In addition, the space of multipliers is analyzed. 
@article{TM_2002_236_a26,
     author = {M. I. Neiman-Zade and A. M. Savchuk},
     title = {Schr\"odinger {Operators} with {Singular} {Potentials}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {262--271},
     publisher = {mathdoc},
     volume = {236},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2002_236_a26/}
}
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M. I. Neiman-Zade; A. M. Savchuk. Schr\"odinger Operators with Singular Potentials. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 262-271. http://geodesic.mathdoc.fr/item/TM_2002_236_a26/