Invertible linear relations generated by an integral equation with Nevanlinna measure |
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Authors: | V M Bruk |
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Institution: | 1. Saratov State Technical University, ul. Politekhnicheskaya 77, Saratov, 410054, Russia
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Abstract: | We define families of maximal and minimal relations generated by integral equations with Nevanlinna operator measure and non-selfadjoint operator measure. We prove that if a restriction of a maximal relation is continuously invertible, then the inverse operator is integral. We study the case when the convergence of non-selfadjoint operator measures implies the convergence of the corresponding integral operators inverse to restrictions of maximal relations, and establish a sufficient condition for the validity of this implication. The obtained results are applicable to the study of differential equations with singular potentials. |
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