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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, Number 2, Pages 16–29
(Mi ivm8771)
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This article is cited in 5 scientific papers (total in 5 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
Abstract:
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.
Keywords:
Hilbert space, linear relation, integral equation, holomorphic family of relations, resolvent convergence.
Received: 22.01.2012
Citation:
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
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https://www.mathnet.ru/eng/ivm8771 https://www.mathnet.ru/eng/ivm/y2013/i2/p16
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Abstract page: | 429 | Full-text PDF : | 79 | References: | 60 | First page: | 11 |
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