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

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.

UDC: 517.968.25

Received: 18.10.2013
Revised: 17.04.2014

DOI: 10.4213/mzm10397

 English version: Mathematical Notes, 2014, 96:6, 914–920

Bibliographic databases:

• 
• 
• 
• 
•