On a transformation of integral equations
- Authors: Yengibaryan B.N.1, Yengibaryan N.B.1
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Affiliations:
- Institute of Mathematics of NAS of Armenia
- Issue: Vol 52, No 6 (2017)
- Pages: 288-294
- Section: Integral Equations
- URL: https://journals.rcsi.science/1068-3623/article/view/228100
- DOI: https://doi.org/10.3103/S1068362317060048
- ID: 228100
Cite item
Abstract
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.
About the authors
B. N. Yengibaryan
Institute of Mathematics of NAS of Armenia
Author for correspondence.
Email: b.yengibaryan@eif.am
Armenia, Yerevan
N. B. Yengibaryan
Institute of Mathematics of NAS of Armenia
Email: b.yengibaryan@eif.am
Armenia, Yerevan