Izv. Vyssh. Uchebn. Zaved. Mat., 2013, Number 2, Pages 16–29
This article is cited in 4 scientific papers (total in 4 papers)
Invertible linear relations generated by an integral equation with a Nevanlinna measure
V. M. Bruk
Chair of Mathematics and Modeling, Saratov State Technical University, Saratov, Russia
We define families of maximal and minimal relations generated by integral equations with a Nevanlinna operator measure and a non-selfadjoint operator measure. We prove that if a restriction of a maximal relation is continuously invertible, then the operator inverse to this restriction is integral. We establish a sufficient condition ensuring that the convergence of non-selfadjoint operator measures implies the convergence of the corresponding integral operators inverse to restrictions of maximal relations. The obtained results are applicable to differential equations with singular coefficients.
Hilbert space, linear relation, integral equation, holomorphic family of relations, resolvent convergence.
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Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:2, 13–24
V. M. Bruk, “Invertible linear relations generated by an integral equation with a Nevanlinna measure”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 2, 16–29; Russian Math. (Iz. VUZ), 57:2 (2013), 13–24
Citation in format AMSBIB
\paper Invertible linear relations generated by an integral equation with a~Nevanlinna measure
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\jour Russian Math. (Iz. VUZ)
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This publication is cited in the following articles:
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”, Zhurn. matem. fiz., anal., geom., 9:4 (2013), 496–535
V. M. Bruk, “On the Characteristic Operator of an Integral Equation with a Nevanlinna Measure in the Infinite-Dimensional Case”, Zhurn. matem. fiz., anal., geom., 10:2 (2014), 163–188
V. M. Bruk, “On Linear Relations Generated by an Integro-Differential Equation with Nevanlinna Measure in the Infinite-Dimensional Case”, Math. Notes, 96:1 (2014), 10–25
V. M. Bruk, “Invertibility of linear relations generated by integral equation with operator measures”, Ufa Math. J., 6:4 (2014), 48–59
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