Geodesic
Invertibility of linear relations generated by integral equation with operator measures
Ufa mathematical journal, Tome 6 (2014) no. 4, pp. 48-59

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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
Mots-clés : impulse action. 
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     author = {V. M. Bruk},
     title = {Invertibility of linear relations generated by integral equation with operator measures},
     journal = {Ufa mathematical journal},
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     url = {http://geodesic.mathdoc.fr/item/UFA_2014_6_4_a3/}
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V. M. Bruk. Invertibility of linear relations generated by integral equation with operator measures. Ufa mathematical journal, Tome 6 (2014) no. 4, pp. 48-59. http://geodesic.mathdoc.fr/item/UFA_2014_6_4_a3/