Geodesic
A Criterion for the Unconditional Basis Property of Eigenvectors for Finite-Rank Perturbations of Volterra Operators
Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 2, pp. 86-91.

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A criterion for the unconditional basis property of eigenvectors for finite-rank perturbations of Volterra operators is given. Considerations are based on functional models for non-self-adjoint operators and on the technique of the Muckenhoupt matrix weights.
Keywords: unconditional basis, non-self-adjoint operators, entire inner matrix functions, Muckenhoupt matrix weights. 
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     title = {A {Criterion} for the {Unconditional} {Basis} {Property} of {Eigenvectors} for {Finite-Rank} {Perturbations} of {Volterra} {Operators}},
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G. M. Gubreev; A. A. Tarasenko. A Criterion for the Unconditional Basis Property of Eigenvectors for Finite-Rank Perturbations of Volterra Operators. Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 2, pp. 86-91. http://geodesic.mathdoc.fr/item/FAA_2011_45_2_a5/

[1] G. M. Gubreev, Yu. D. Latushkin, Funkts. analiz i ego pril., 42:3 (2008), 85–89 | DOI | MR | Zbl

[2] S. Treil, A. Volberg, J. Funct. Anal., 143:2 (1997), 269–308 | DOI | MR | Zbl

[3] M. S. Brodskii, Treugolnye i zhordanovy predstavleniya lineinykh operatorov, Nauka, M., 1969 | MR

[4] B. Sekefalvi-Nad, Ch. Foyash, Garmonicheskii analiz operatorov v gilbertovom prostranstve, Mir, M., 1970 | MR

[5] D. Garnett, Ogranichennye analiticheskie funktsii, Mir, M., 1984 | MR | Zbl

[6] N. K. Nikolskii, Teoriya operatorov v funktsionalnykh prostranstvakh, Nauka, Novosibirsk, 1977, 240–282

[7] S. R. Treil, DAN SSSR, 288:2 (1986), 308–312 | MR | Zbl

[8] N. K. Nikolskii, B. S. Pavlov, Izv. AN SSSR, 34:1 (1970), 90–133 | MR

[9] B. S. Pavlov, DAN SSSR, 247:1 (1979), 37–40 | MR | Zbl

[10] S. A. Avdonin, S. A. Ivanov, Families of Exponentials, Cambridge Univ. Press, 1995 | MR | Zbl

[11] M. M. Dzhrbashyan, Izv. AN Arm. SSR, 5:2 (1970), 71–96 | MR | Zbl