Geodesic
Generalized resolvents of linear relations generated by a nonnegative operator function and a differential elliptic-type expression
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2008), pp. 12-26

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We study invertible extensions of the minimal relation generated by a nonnegative operator function and a differential elliptic-type expression. We prove that the operators inverse to such extensions are integral operators and describe such integral operators. We obtain a formula for generalized resolvents of the minimal relation.
Keywords: linear relation, symmetric relation, generalized resolvent, Green function, operator function. 
@article{IVM_2008_11_a1,
     author = {V. M. Bruk},
     title = {Generalized resolvents of linear relations generated by a nonnegative operator function and a differential elliptic-type expression},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {12--26},
     publisher = {mathdoc},
     number = {11},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_11_a1/}
}
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V. M. Bruk. Generalized resolvents of linear relations generated by a nonnegative operator function and a differential elliptic-type expression. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2008), pp. 12-26. http://geodesic.mathdoc.fr/item/IVM_2008_11_a1/