This article is cited in 3 papers

Dissipative extensions of linear relations generated by integral equations with operator measures

Vladislav M. Bruk

Saratov State Technical University, 77 Politekhnicheskaya str., Saratov 410054, Russia

Abstract: In the paper, a minimal relation $L_0$ generated by an integral equation with operator measures is defined and a description of the adjoint relation $L_0^*$ is given. For this minimal relation, we construct a space of boundary values (a boundary triplet) satisfying the abstract “Green formula” and get a description of maximal dissipative (accumulative) and also self-adjoint extensions of the minimal relation.

Key words and phrases: Hilbert space, linear relation, integral equation, dissipative extension, self-adjoint extension, boundary value, operator measure.

MSC: 47A10, 46G12, 45N05

Received: 26.10.2019
Revised: 10.12.2019

Language: English

DOI: 10.15407/mag16.04.381

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