Geodesic
Existence and basis property of eigen and associated elements of linear operators
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2008), pp. 43-55.

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In this paper we continue the study described earlier in No. 5, 2006, of Russian Mathematics (Iz. VUZ). We establish conditions, providing the asymptotics mentioned in the cited paper. We prove the basis property of eigen functions and associated ones in linear problems for differential equations with deviating arguments.
Keywords: the asymptotics of eigenvalues, the basis property, eigen and associated elements. 
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V. S. Mokeichev. Existence and basis property of eigen and associated elements of linear operators. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2008), pp. 43-55. http://geodesic.mathdoc.fr/item/IVM_2008_6_a4/

[1] Mokeichev V. S., “Dokazatelstvo bazisnosti s ispolzovaniem tolko asimptotiki sobstvennykh i prisoedinennykh elementov”, Izv. vuzov. Matematika, 2006, no. 5, 48–54 | MR

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[5] Mokeichev V. S., “Bazisnost v smysle Rissa sobstvennykh i prisoedinennykh elementov”, Sovremennye problemy teorii funktsii i ikh prilozheniya, Tez. dokl. 12-i Sarat. zimnei shkoly, Saratov, 2004, 124–125 | MR