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On a transformation of integral equations. (English. Russian original) Zbl 1390.45004
J. Contemp. Math. Anal., Armen. Acad. Sci. 52, No. 6, 288-294 (2017); translation from Izv. Nats. Akad. Nauk Armen., Mat. 52, No. 6, 3-11 (2017).
Summary: Let \(E = E(a,b)\) be some Banach space of measurable functions on \((a,b)\), \(I\) be the identity operator, and let \(\hat K\) be a Fredholm-type regular integral operator acting on \(E\) and \(\hat{K}_\pm\) be its triangular parts. We consider the representation \(I - \hat K = \left( {I - {{\hat K}_ - }} \right)\left( {I - \hat U} \right)\left( {I - {{\hat K}_ + }} \right)\), for some known classes of integral operators. In particular,we show that under certain conditions the operator \(\hat U\) is positive and its spectral radius satisfies the condition \(r\left( {\hat U} \right) < 1\). Also, we give some possible applications of the representation.
MSC:
45A05 Linear integral equations
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