Geodesic
On an Algebra of Multidimensional Integral Operators with Homogeneous-Difference Kernels
Matematičeskie zametki, Tome 95 (2014) no. 2, pp. 163-169.

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A Banach algebra generated by multidimensional integral operators with homogeneous-difference kernels is considered. A symbolic calculus is constructed for this algebra and, in terms of this calculus, necessary and sufficient conditions for the invertibility of an operator are obtained.
Keywords: multidimensional integral operator, homogeneous-difference kernel, symbolic calculus, invertibility. 
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O. G. Avsyankin. On an Algebra of Multidimensional Integral Operators with Homogeneous-Difference Kernels. Matematičeskie zametki, Tome 95 (2014) no. 2, pp. 163-169. http://geodesic.mathdoc.fr/item/MZM_2014_95_2_a0/

[1] N. Karapetiants, S. Samko, Equations with Involutive Operators, Birkhäuser Boston, Boston, MA, 2001 | MR | Zbl

[2] O. G. Avsyankin, “Ob algebre parnykh integralnykh operatorov s odnorodnymi yadrami”, Matem. zametki, 73:4 (2003), 483–493 | DOI | MR | Zbl

[3] O. G. Avsyankin, N. K. Karapetyants, “Proektsionnyi metod v teorii integralnykh operatorov s odnorodnymi yadrami”, Matem. zametki, 75:2 (2004), 163–172 | DOI | MR | Zbl

[4] O. G. Avsyankin, “O $C^*$-algebre, porozhdennoi mnogomernymi integralnymi operatorami s odnorodnymi yadrami i operatorami multiplikativnogo sdviga”, Dokl. RAN, 419:6 (2008), 727–728 | MR | Zbl

[5] O. G. Avsyankin, “Mnogomernye integralnye operatory s odnorodno-raznostnymi yadrami”, Differents. uravneniya, 48:1 (2012), 64–69 | Zbl

[6] V. N. Berkovich, “Nestatsionarnaya smeshannaya zadacha dinamiki neodnorodno uprugoi klinovidnoi sredy”, Ekologicheskii vestnik nauchnykh tsentrov Chernomorskogo ekonomicheskogo soobschestva, 2005, no. 3, 17–21

[7] N. Danford, Dzh. Shvarts, Lineinye operatory. T. 2. Spektralnaya teoriya, IL, M., 1966 | MR | Zbl

[8] I. M. Gelfand, D. A. Raikov, G. E. Shilov, Kommutativnye normirovannye koltsa, Sovremennye problemy matematiki, Fizmatgiz, M., 1960 | MR | Zbl