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.
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