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Matematicheskie Zametki, 2014, Volume 96, Issue 6, Pages 849–855
DOI: https://doi.org/10.4213/mzm10397 (Mi mzm10397) 		 
On a Criterion for the Invertibility of Integral Operators of the Second Kind in the Space of Summable Functions on the Semiaxis

G. A. Grigoryan

Institute of Mathematics, National Academy of Sciences of Armenia
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DOI: https://doi.org/10.4213/mzm10397
Abstract: 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.
Received: 18.10.2013
Revised: 17.04.2014
English version:
Mathematical Notes, 2014, Volume 96, Issue 6, Pages 914–920
DOI: https://doi.org/10.1134/S0001434614110285
Bibliographic databases:
Document Type: Article
UDC: 517.968.25
Language: Russian
Citation: 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”, Mat. Zametki, 96:6 (2014), 849–855; Math. Notes, 96:6 (2014), 914–920
Citation in format AMSBIB
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