Journal of Mathematical Physics, Analysis, Geometry
2020, vol. 16, No 4, pp. 381-401   https://doi.org/10.15407/mag16.04.381     ( to contents , go back )
https://doi.org/10.15407/mag16.04.381

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
E-mail: vladislavbruk@mail.ru

Received October 26, 2019, revised December 10, 2019.

Abstract

In the paper, a minimal relation L0 generated by an integral equation with operator measures is defined and a description of the adjoint relation L0* 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.

Mathematics Subject Classification 2010: 47A10, 46G12, 45N05
Key words: Hilbert space, linear relation, integral equation, dissipative extension, self-adjoint extension, boundary value, operator measure

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