This article is cited 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.

UDC: 517.983

MSC: 46G12, 45N05, 47A10

Received: 04.04.2018
Revised: 08.08.2018
Accepted: 11.08.2018

Language: English

DOI: 10.15393/j3.art.2018.4630

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