Geodesic
Generalized resolvents of operators generated by integral equations
Problemy analiza, Tome 7 (2018) no. 2, pp. 20-38

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We define a minimal operator $L_{0}$ generated by an integral equation with an operator measure and give a description of the adjoint operator $L^{*}_{0}$. We prove that every generalized resolvent of $L_{0}$ is an integral operator and give a description of boundary value problems associated to generalized resolvents.
Keywords: integral equation, Hilbert space, symmetric operator, generalized resolvent, boundary value problem. 
@article{PA_2018_7_2_a1,
     author = {V. M. Bruk},
     title = {Generalized resolvents of operators generated by integral equations},
     journal = {Problemy analiza},
     pages = {20--38},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2018_7_2_a1/}
}
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V. M. Bruk. Generalized resolvents of operators generated by integral equations. Problemy analiza, Tome 7 (2018) no. 2, pp. 20-38. http://geodesic.mathdoc.fr/item/PA_2018_7_2_a1/