Geodesic
On a Criterion for the Invertibility of Integral Operators of the Second Kind in the Space of Summable Functions on the Semiaxis
Matematičeskie zametki, Tome 96 (2014) no. 6, pp. 849-855

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To establish a criterion for the invertibility of integral operators of the second kind in terms of the kernel of the integral part of this operator, a special factorization method is applied. We present a transformation reducing the problem of the invertibility of such an operator to that of the inversion of an integral operator of the second kind with contracting integral part.
Keywords: criterion for the invertibility of integral operators, integral operator of the second kind, contraction operator, invertibility conditions. 
@article{MZM_2014_96_6_a3,
     author = {G. A. Grigoryan},
     title = {On a {Criterion} for the {Invertibility} of {Integral} {Operators} of the {Second} {Kind} in the {Space} of {Summable} {Functions} on the {Semiaxis}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {849--855},
     publisher = {mathdoc},
     volume = {96},
     number = {6},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_6_a3/}
}
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G. A. Grigoryan. On a Criterion for the Invertibility of Integral Operators of the Second Kind in the Space of Summable Functions on the Semiaxis. Matematičeskie zametki, Tome 96 (2014) no. 6, pp. 849-855. http://geodesic.mathdoc.fr/item/MZM_2014_96_6_a3/