Geodesic
A~criterion for unitary equivalence of unbounded operators to integral operators
Matematičeskie zametki, Tome 23 (1978) no. 2, pp. 271-280.

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Necessary and sufficient conditions are established for unitary equivalence of unbounded non-self-adjoint linear operators with Carleman and $B$-Carleman integral operators. 
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     author = {V. B. Korotkov},
     title = {A~criterion for unitary equivalence of unbounded operators to integral operators},
     journal = {Matemati\v{c}eskie zametki},
     pages = {271--280},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_2_a10/}
}
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V. B. Korotkov. A~criterion for unitary equivalence of unbounded operators to integral operators. Matematičeskie zametki, Tome 23 (1978) no. 2, pp. 271-280. http://geodesic.mathdoc.fr/item/MZM_1978_23_2_a10/