The unitary equivalence of linear operatops to integral operators
Matematičeskie zametki, Tome 19 (1976) no. 4, pp. 601-610.

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Criteria are established for the unitary equivalence of bounded linear operators to B-Carleman and bi-Carleman integral operators.
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     author = {V. B. Korotkov},
     title = {The unitary equivalence of linear operatops to integral operators},
     journal = {Matemati\v{c}eskie zametki},
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V. B. Korotkov. The unitary equivalence of linear operatops to integral operators. Matematičeskie zametki, Tome 19 (1976) no. 4, pp. 601-610. http://geodesic.mathdoc.fr/item/MZM_1976_19_4_a13/