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Invertibility of linear relations generated by integral equation with operator measures
V. M. Bruk Saratov State Technical University, Saratov, Russia
Abstract:
We investigate linear relations generated by an integral equation with operator measures on a segment in the infinite-dimensional case. In terms of boundary values, we obtain necessary and sufficient conditions.
We consider integral equation with operator measures on a bounded closed interval in the infinite-dimensional case. In terms of boundary values, we obtain necessary and sufficient conditions under which these relations $S$ possess the properties: $S$ is closed relation; $S$ is invertible relation; the kernel of $S$ is finite-dimensional; the range of $S$ is closed; $S$ is continuously invertible relation and others. The results are applied to a system of integral equations becoming a quasidifferential equation whenever the operator measures are absolutely continuous as well as to an integral equation with multi-valued impulse action.
Keywords:
integral equation, operator measure, Hilbert space, linear relation, spectrum, quasiderivative, impulse action.
Received: 15.05.2014
Citation:
V. M. Bruk, “Invertibility of linear relations generated by integral equation with operator measures”, Ufimsk. Mat. Zh., 6:4 (2014), 50–62; Ufa Math. J., 6:4 (2014), 48–59
Linking options:
https://www.mathnet.ru/eng/ufa259https://doi.org/10.13108/2014-6-4-48 https://www.mathnet.ru/eng/ufa/v6/i4/p50
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Abstract page: | 277 | Russian version PDF: | 126 | English version PDF: | 6 | References: | 38 |
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