Generalized resolvents of operators generated by integral equations
Problemy analiza, Tome 7 (2018) no. 2, pp. 20-38.

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We define a minimal operator $L_{0}$ generated by an integral equation with an operator measure and give a description of the adjoint operator $L^{*}_{0}$. We prove that every generalized resolvent of $L_{0}$ 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.
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V. M. Bruk. Generalized resolvents of operators generated by integral equations. Problemy analiza, Tome 7 (2018) no. 2, pp. 20-38. http://geodesic.mathdoc.fr/item/PA_2018_7_2_a1/

[1] Vishcha Shkola, Kharkiv, 1978 | MR | Zbl

[2] Uspekhi Mat. Nauk, 68:1 (2013), 77–128 | DOI | DOI | MR | Zbl

[3] Naukova Dumka, Kiev, 1965 | MR | Zbl

[4] Mat. Zametki, 15:6 (1974), 945–954 | DOI | MR | Zbl

[5] Mat. Sbornik, 100:2 (1976), 210–216 | DOI | MR

[6] Bruk V. M., “On Boundary Value Problems Associated with Holomorphic Families of Operators”, Funct. Anal., 29, Ulyanovsk, 1989, 32–42 (in Russian) | MR | Zbl

[7] Bruk V. M., “Boundary Value Problems for Integral Equations with Operator Measures”, Probl. Anal. Issues Anal., 6(24):1 (2017), 19–40 | DOI | MR | Zbl

[8] Bruk V. M., “On Self-Adjoint Extensions of Operators Generated by Integral Equations”, Taurida Journal of Comp. Science Theory and Math., 2017, no. 1, 17–31 http://tvim.info/

[9] Naukova Dumka, Kiev, 1984 | MR | Zbl

[10] Khrabustovskyi V., “Analogs of Generalized Resolvents for Relations Generated by a Pair of Differential Operator Expressions One of which Depends on Spectral Parameter in Nonlinear Manner”, Journal of Mathematical Physics, Analysis, Geometry, 9:4 (2013), 496–535 | MR | Zbl

[11] Mat. Zametki, 17:1 (1975), 41–48 | DOI | MR

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

[13] Straus A. V., “On Generalized Resolvents and Spectral Functions of Differential Operators of Even Order”, Izv. Akad. Nauk SSSR, Ser. Matem., 21:6 (1957), 785–808 | MR