Geodesic
Invertible linear relations generated by an integral equation with a~Nevanlinna measure
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2013), pp. 16-29

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We define families of maximal and minimal relations generated by integral equations with a Nevanlinna operator measure and a non-selfadjoint operator measure. We prove that if a restriction of a maximal relation is continuously invertible, then the operator inverse to this restriction is integral. We establish a sufficient condition ensuring that the convergence of non-selfadjoint operator measures implies the convergence of the corresponding integral operators inverse to restrictions of maximal relations. The obtained results are applicable to differential equations with singular coefficients.
Keywords: Hilbert space, linear relation, integral equation, holomorphic family of relations, resolvent convergence. 
@article{IVM_2013_2_a1,
     author = {V. M. Bruk},
     title = {Invertible linear relations generated by an integral equation with {a~Nevanlinna} measure},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {16--29},
     publisher = {mathdoc},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_2_a1/}
}
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V. M. Bruk. Invertible linear relations generated by an integral equation with a~Nevanlinna measure. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2013), pp. 16-29. http://geodesic.mathdoc.fr/item/IVM_2013_2_a1/