Journal of Mathematical Physics, Analysis, Geometry
2020, vol. 16, No 4, pp. 381-401     ( to contents , go back )

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

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


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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