Abstract:
We define a minimal operator L0L0 generated by an integral equation with an operator measure and give a description of the adjoint operator L∗0L∗0.
We prove that every generalized resolvent of L0L0 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.
\Bibitem{Bru18}
\by V.~M.~Bruk
\paper Generalized resolvents of operators generated by integral equations
\jour Probl. Anal. Issues Anal.
\yr 2018
\vol 7(25)
\issue 2
\pages 20--38
\mathnet{http://mi.mathnet.ru/pa245}
\crossref{https://doi.org/10.15393/j3.art.2018.4630}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000454220100002}
\elib{https://elibrary.ru/item.asp?id=36744240}
Linking options:
https://www.mathnet.ru/eng/pa245
https://www.mathnet.ru/eng/pa/v25/i2/p20
This publication is cited in the following 5 articles:
Vladislav Bruk, “Linear relations generated by integral equations with Nevanlinna operator measures”, Filomat, 38:4 (2024), 1153
Vladislav Bruk, “On characteristic functions of generalized resolvents generated by integral equations with operator measures”, Filomat, 37:23 (2023), 7699
Vladislav Bruk, “Generalized resolvents of linear relations generated by integral equations with operator measures”, Filomat, 36:14 (2022), 4793
V. M. Bruk, “On self-adjoint and invertible linear relations generated by integral equations”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2020, no. 1, 106–121
Vladislav M. Bruk, “Dissipative extensions of linear relations generated by integral equations with operator measures”, Zhurn. matem. fiz., anal., geom., 16:4 (2020), 381–401
Citation in format AMSBIB
Contact us: