Geodesic
Dissipative extensions of linear relations generated by integral equations with operator measures
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 16 (2020) no. 4, pp. 381-401 
Vladislav M. Bruk. Dissipative extensions of linear relations generated by integral equations with operator measures. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 16 (2020) no. 4, pp. 381-401. http://geodesic.mathdoc.fr/item/JMAG_2020_16_4_a0/
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     url = {http://geodesic.mathdoc.fr/item/JMAG_2020_16_4_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Russian Math. Surveys, 68:1 (2013), 69–116 | DOI | DOI | MR | Zbl

[2] Amer. Math. Soc., Providence, RI | MR | Zbl

[3] J. Behrndt, S. Hassi, H. Snoo, R. Wietsma, “Square-integrable solutions and Weil functions for singular canonical systems”, Math. Nachr., 284:11–12 (2011), 1334–1384 | DOI | MR | Zbl

[4] Math. USSR-Sbornik, 29:2 (1976), 186–192 | DOI | MR | Zbl

[5] Mathematical Notes, 22:6 (1977), 953–958 | DOI | MR | Zbl

[6] V.M. Bruk, “On a number of linearly independent square-integrable solutions of systems of differential equations”, Functional Analysis, 5, Uljanovsk, 1975, 25–33 | MR

[7] Mathematical Notes, 24:4 (1978), 767–773 | DOI | MR | Zbl

[8] V.M. Bruk, “Boundary value problems for integral equations with operator measures”, Probl. Anal. Issues Anal., 6(24):1 (2017), 19–40 | DOI | MR | Zbl

[9] V.M. Bruk, “On self-adjoint extensions of operators generated by integral equations”, Taurida Journal of Computer Science Theory and Mathematics, 2017, no. 1(34), 17–31

[10] V.M. Bruk, “On the characteristic operator of an integral equation with a Nevanlinna measure in the infinite-dimensional case”, Zh. Mat. Fiz. Anal. Geom., 10:2 (2014), 163–188 | DOI | MR | Zbl

[11] V.M. Bruk, “Generalized Resolvents of operators generated by integral equations”, Probl. Anal. Issues Anal., 7(25):2 (2018), 20–38 | DOI | MR | Zbl

[12] V.M. Bruk, “On self-adjoint extensions of relations generated by integral equations”, Taurida Journal of Computer Science Theory and Mathematics, 2019, no. 1(42), 43–61

[13] Kluwer Acad. Publ., Dordrecht–Boston–London | MR | Zbl

[14] Soviet Math. Dokl., 13:1 (1972), 1063–1067 | MR | Zbl

[15] V. Khrabustovskyi, “Analogs of generalized resolvents for relations generated by a pair of differential operator expressions one of which depends on spectral parameter in nonlinear manner”, Zh. Mat. Fiz. Anal. Geom., 9:4 (2013), 496–535 | MR | Zbl

[16] Mathematical Notes, 17:1 (1975), 25–28 | DOI | MR

[17] M.G. Krein, “The theory of self-adjoint extensions of semi-bounded Hermitian transformations and its applications”, Mat. Sbornik, 20:3 (1947), 431–495 | MR | Zbl

[18] George G. Harrar and Company, LTD, London–Toronto–Wellington–Sidney | MR | Zbl

[19] B.C. Orcutt, Canonical Differential Equations, Ph. D. Thesis, University of Virginia, 1969 | MR

[20] Soviet Math. Dokl., 10:1 (1969), 188–192 | MR | Zbl

[21] F.S. Rofe-Beketov, A.M Kholkin, Spectral Analysis of Differential Operators, World Scientific Monograph Series in Mathematics, 7, Singapure, 2005 | DOI | MR | Zbl