Geodesic
Uniqueness theorems and essentially self-adjoint operators
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part X, Tome 107 (1982), pp. 169-177 
S. V. Khrushchev. Uniqueness theorems and essentially self-adjoint operators. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part X, Tome 107 (1982), pp. 169-177. http://geodesic.mathdoc.fr/item/ZNSL_1982_107_a10/
@article{ZNSL_1982_107_a10,
     author = {S. V. Khrushchev},
     title = {Uniqueness theorems and essentially self-adjoint operators},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {169--177},
     year = {1982},
     volume = {107},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_107_a10/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The paper deals with an extension of well-known Nussbaum's and Kelson's theorems. It is shown that sets of uniqueness for the boundary values of functions, smooth in the closed upper half-plane and holomorphic in its interior, are closely related with tests of essentially self-adjointness for semi-bounded symmetric operators in Hilbert space.