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 Tr. Mat. Inst. Steklova, 2012, Volume 278, Pages 59–67 (Mi tm3398)

Topological methods in solvability theory of multidimensional pair integral operators with homogeneous kernels of compact type

V. M. Deundyak

Southern Federal University, Rostov-on-Don, Russia

Abstract: The problem of getting effective Fredholm conditions for operators with bihomogeneous kernels reduces to the question of invertibility for families of operators with homogeneous kernels and to the calculation of homotopy invariants for spaces of Fredholm and invertible operators of that type. The purpose of the present paper is to study integral operators with homogeneous kernels of compact type in $L_p(\mathbb R^n)$, $1<p<+\infty$. The classes of homotopy equivalence for the spaces of Fredholm and invertible operators in the $C^*$-algebra of pair operators with homogeneous kernels of compact type are calculated by means of operator $K$-theory.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2012, 278, 51–59

Bibliographic databases:

UDC: 517.9
Received in February 2011

Citation: V. M. Deundyak, “Topological methods in solvability theory of multidimensional pair integral operators with homogeneous kernels of compact type”, Differential equations and dynamical systems, Collected papers, Tr. Mat. Inst. Steklova, 278, MAIK Nauka/Interperiodica, Moscow, 2012, 59–67; Proc. Steklov Inst. Math., 278 (2012), 51–59

Citation in format AMSBIB
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This publication is cited in the following articles:
1. V. M. Deundyak, E. A. Romanenko, “Fredgolmovost sostavnykh dvumernykh integralnykh operatorov s odnorodnymi yadrami singulyarnogo tipa v prostranstve $L_p$”, Vestnik Donskogo gosudarstvennogo tekhnicheskogo universiteta, 14:1 (76) (2014), 22–33
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