Abstract:
We introduce the class $B_0$ of linear operators in $L_2$ satisfying the generalized von Neumann condition. Various sufficient conditions are established for the membership of operators in the class $B_0$. Linear functional equations of the first and second kind in $L_2$ with operators of class $B_0$ are considered.
Keywords:closable operator, limit spectrum, generalized von Neumann condition, linear functional equation of the first or second kind, integral equation of the first or second kind.
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