### On Multiple Bases of Eigen and Associated Vectors of Operator Pencils in the Hilbert Spaces

Received: 4 May 2015     Accepted: 19 May 2015     Published: 21 August 2015
Abstract

It is proved the theorem about of multiple basis of eigen and associated vectors of the operator pencil, non-linear depending on parameter in the Hilbert space. This work is the generalization of existing results on the multiple completeness of the eigen and associated vectors of polynomial pencils, rationally depending on parameters. At the proof the author uses the methods of spectral theory of operators

Keywords

Multiple Basis, Eigen And Associated, Residue, Bounded

References
 [1] Keldysh M.V. About completeness of eigen functions of some class linear non-selfadjoint operators. Journal:Success of Mathematical Science , 1971, т.27, issue.4, pp.15-47 [2] Dzhabarzadeh R.M. On expansions series on eigen and associated vectors of operator pencils, Journal: Scientific notes of Azerb.State University,1964, №3,pp.75-81. [3] Vizitei V.N., Markus A.S.. On convergence of multiple expansions on the system of eigen and associated vectors of polynomial pencils Mathematical collection,1965,т.66, №2,pp..287-320 [4] Gokhberg I. Ts., Kreyn M.Q. Introduction to the theory of linear non-selfadjoint operators in the Hilbert space.Moscow, 1964, pp 1-433 [5] Allakhverdiev J.E., Dzhabarzadeh R. M. // Spectral theory of operator pencil in the Hilbert space.ДAN of Azerbaijan - 2011, т.LXVII, № 4.- pр.3-10 [6] Allakhverdiev J.E. Dzhabarzadeh R.M. Оn summation of multiple series on eigen and associated vectors operator pensilw by Abel?s method. ДАN Аz. SSR, 1979,т.35, № 7, p 19-23.. [7] Allakhverdiev J E. The evolution of resolvents and the theorems on completeness of oerators, depending on spectral parameters. Transactionof AN of Azerb. SSR , seria of physics -tekhnics and mathematical sciences,1074,6,pp.3-36 [8] Lidskii. About summation of the series on the general vectors of the non-selfadjoint operators. Proceeding of Moscow Scientific Society, t.11,1962 [9] Askerov N.Q.,Kreyn S.Q., Laptev Q.I. On some class of non-selfadjoint boundary problems. DAN, 155, 3 (1964),499-502
• APA Style

Rakhshanda Dzhabarzadeh. (2015). On Multiple Bases of Eigen and Associated Vectors of Operator Pencils in the Hilbert Spaces. Pure and Applied Mathematics Journal, 4(4-1), 27-32. https://doi.org/10.11648/j.pamj.s.2015040401.16

ACS Style

Rakhshanda Dzhabarzadeh. On Multiple Bases of Eigen and Associated Vectors of Operator Pencils in the Hilbert Spaces. Pure Appl. Math. J. 2015, 4(4-1), 27-32. doi: 10.11648/j.pamj.s.2015040401.16

AMA Style

Rakhshanda Dzhabarzadeh. On Multiple Bases of Eigen and Associated Vectors of Operator Pencils in the Hilbert Spaces. Pure Appl Math J. 2015;4(4-1):27-32. doi: 10.11648/j.pamj.s.2015040401.16

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journal = {Pure and Applied Mathematics Journal},
volume = {4},
number = {4-1},
pages = {27-32},
doi = {10.11648/j.pamj.s.2015040401.16},
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abstract = {It is proved the theorem about of multiple basis of eigen and associated vectors of the operator pencil, non-linear depending on parameter in the Hilbert space. This work is the generalization of existing results on the multiple completeness of the eigen and associated vectors of polynomial pencils, rationally depending on parameters. At the proof the author uses the methods of spectral theory of operators},
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AB  - It is proved the theorem about of multiple basis of eigen and associated vectors of the operator pencil, non-linear depending on parameter in the Hilbert space. This work is the generalization of existing results on the multiple completeness of the eigen and associated vectors of polynomial pencils, rationally depending on parameters. At the proof the author uses the methods of spectral theory of operators
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Author Information
• Department of functional analysis. Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan

• Sections