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This article is cited in 5 scientific papers (total in 5 papers)
Generalized resolvents of operators generated by integral equations
V. M. Bruk Saratov State Technical University,
77, Politehnicheskaja str., Saratov 410054, Russia
Abstract:
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.
Received: 04.04.2018 Revised: 08.08.2018 Accepted: 11.08.2018
Citation:
V. M. Bruk, “Generalized resolvents of operators generated by integral equations”, Probl. Anal. Issues Anal., 7(25):2 (2018), 20–38
Linking options:
https://www.mathnet.ru/eng/pa245 https://www.mathnet.ru/eng/pa/v25/i2/p20
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