Аннотация:
We define the families of maximal and minimal relations generated by an integral equation with a Nevanlinna operator measure in the infinite-dimensional case and prove their holomorphic property. We show that if the restrictions of maximal relations are continuously invertible, then the operators inverse to these restrictions are integral. By using these results, we prove the existence of the characteristic operator and describe the families of linear relations generating the characteristic operator.
Ключевые слова и фразы:
Hilbert space, linear relation, integral equation, characteristic operator, Nevanlinna measure.
Поступила в редакцию: 19.01.2013 Исправленный вариант: 20.08.2013
Образец цитирования:
V. M. Bruk, “On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the Infinite-Dimensional Case”, Журн. матем. физ., анал., геом., 10:2 (2014), 163–188
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\paper On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the Infinite-Dimensional Case
\jour Журн. матем. физ., анал., геом.
\yr 2014
\vol 10
\issue 2
\pages 163--188
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/jmag587
https://www.mathnet.ru/rus/jmag/v10/i2/p163
Эта публикация цитируется в следующих 9 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
D. V. Tretyakov, Yu. L. Kudryashov, “On a General Approach to Construction of a Self-Adjoint Dilation for a Dissipative Operator”, J Math Sci, 268:6 (2022), 816
Vladislav Bruk, “Generalized resolvents of linear relations generated by integral equations with operator measures”, Filomat, 36:14 (2022), 4793
Bruk V.M., “Invertible Linear Relations Generated By Integral Equations With Operator Measures”, Filomat, 35:5 (2021), 1589–1607
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
О. H. Storozh, “Solvable Extensions of Some Nondensely Defined Operators and the Resolvents of These Extensions”, J Math Sci, 240:1 (2019), 1
V. M. Bruk, “Boundary value problems for integral equations with operator measures”, Пробл. анал. Issues Anal., 6(24):1 (2017), 19–40
V. I. Mogilevskii, “On spectral and pseudospectral functions of first-order symmetric systems”, Уфимск. матем. журн., 7:2 (2015), 123–144; Ufa Math. J., 7:2 (2015), 115–136
Цитирование в формате AMSBIB
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