Аннотация:
We define a minimal operator L0 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 L0 is an integral operator and give a description of boundary value problems associated to generalized resolvents.
Ключевые слова:
integral equation, Hilbert space, symmetric operator, generalized resolvent, boundary value problem.
Поступила в редакцию: 04.04.2018 Исправленный вариант: 08.08.2018 Принята в печать: 11.08.2018
Образец цитирования:
V. M. Bruk, “Generalized resolvents of operators generated by integral equations”, Пробл. анал. Issues Anal., 7(25):2 (2018), 20–38
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\paper Generalized resolvents of operators generated by integral equations
\jour Пробл. анал. Issues Anal.
\yr 2018
\vol 7(25)
\issue 2
\pages 20--38
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\crossref{https://doi.org/10.15393/j3.art.2018.4630}
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Эта публикация цитируется в следующих 5 статьяx:
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”, Журн. матем. физ., анал., геом., 16:4 (2020), 381–401
Цитирование в формате AMSBIB
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