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
| Published in |
Pure and Applied Mathematics Journal (Volume 4, Issue 4-1)
This article belongs to the Special Issue Spectral Theory of Multiparameter Operator Pencils and Its Applications |
| DOI | 10.11648/j.pamj.s.2015040401.16 |
| Page(s) | 27-32 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Multiple Basis, Eigen And Associated, Residue, Bounded
| [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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Download@article{10.11648/j.pamj.s.2015040401.16,
author = {Rakhshanda Dzhabarzadeh},
title = {On Multiple Bases of Eigen and Associated Vectors of Operator Pencils in the Hilbert Spaces},
journal = {Pure and Applied Mathematics Journal},
volume = {4},
number = {4-1},
pages = {27-32},
doi = {10.11648/j.pamj.s.2015040401.16},
url = {https://doi.org/10.11648/j.pamj.s.2015040401.16},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040401.16},
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},
year = {2015}
}
TY - JOUR T1 - On Multiple Bases of Eigen and Associated Vectors of Operator Pencils in the Hilbert Spaces AU - Rakhshanda Dzhabarzadeh Y1 - 2015/08/21 PY - 2015 N1 - https://doi.org/10.11648/j.pamj.s.2015040401.16 DO - 10.11648/j.pamj.s.2015040401.16 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 27 EP - 32 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.s.2015040401.16 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 VL - 4 IS - 4-1 ER -
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