Invertibility of linear relations generated by integral equation with operator measures
V. M. Bruk
Saratov State Technical University, Saratov, Russia
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.
integral equation, operator measure, Hilbert space, linear relation, spectrum, quasiderivative, impulse action.
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Ufa Mathematical Journal, 2014, 6:4, 48–59 (PDF, 384 kB); https://doi.org/10.13108/2014-6-4-48
MSC: 47A06, 47A10, 34B27
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
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\paper Invertibility of linear relations generated by integral equation with operator measures
\jour Ufimsk. Mat. Zh.
\jour Ufa Math. J.
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