Ufa Mathematical Journal
    Volume 6, Number 4, pp. 48-59

    Invertibility of linear relations generated by integral equation with operator measures

    Bruk V.M.


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    We investigate linear relations generated by an integral equ\-a\-tion with operator measures on a segment 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 a closed relation; \(S\) is an invertible relation; the kernel of \(S\) is finite-dimen\-si\-o\-nal; the range of \(S\) is closed; \(S\) is a continuously invertible relation and others. The results are applied to a system of integral equations becoming a quasi-differential equation whenever the operator measures are absolutely continuous as well as to an integral equation with multi-valued impulse action.