The theorem on possibility of multiple summation of the series on eigen and associated vectors of the operator pencil in the Hilbert space is proved. Research of multiple completeness and multiple expansions of eigen and associated vectors of such operator pencils are closely connected with the research of differential operator equation with the boundary conditions
| 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.2015040401.15 |
| Page(s) | 22-26 |
| 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), 2015. Published by Science Publishing Group |
Operator Pencil, Residue, Completely Continuous, Multiple
| [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,p.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 of operator pencils by Abel’s method. ДАN Аz SSR, 1979,т.35, № 7,p 19-23. |
| [7] | Lidskii V.B.. About summation of the series on the general vectors of the non-selfadjoint operators. Proceeding of Moscow Scientific Society, t.11, 1962. |
| [8] | Radzievskii Q.V.Multiple completeness of root vectors of Keldysh’s operator pencil, disturbing by analytical operatorfunction.DAN USSR,ser.A,1976,,7,pp.597-600. |
| [9] | Dzhabarzadeh R. M. To the spectral theory of polynomial pencils.Proceedinfg of Oryol State Universitety Russia ,2006,t.1,pp.161-165. |
APA Style
Rakhshanda Dzhabarzadeh. (2015). Spectral Theory of Operator Pencils in the Hilbert Spaces. Pure and Applied Mathematics Journal, 4(4-1), 22-26. https://doi.org/10.11648/j.pamj.s.2015040401.15
ACS Style
Rakhshanda Dzhabarzadeh. Spectral Theory of Operator Pencils in the Hilbert Spaces. Pure Appl. Math. J. 2015, 4(4-1), 22-26. doi: 10.11648/j.pamj.s.2015040401.15
AMA Style
Rakhshanda Dzhabarzadeh. Spectral Theory of Operator Pencils in the Hilbert Spaces. Pure Appl Math J. 2015;4(4-1):22-26. doi: 10.11648/j.pamj.s.2015040401.15
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Download@article{10.11648/j.pamj.s.2015040401.15,
author = {Rakhshanda Dzhabarzadeh},
title = {Spectral Theory of Operator Pencils in the Hilbert Spaces},
journal = {Pure and Applied Mathematics Journal},
volume = {4},
number = {4-1},
pages = {22-26},
doi = {10.11648/j.pamj.s.2015040401.15},
url = {https://doi.org/10.11648/j.pamj.s.2015040401.15},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040401.15},
abstract = {The theorem on possibility of multiple summation of the series on eigen and associated vectors of the operator pencil in the Hilbert space is proved. Research of multiple completeness and multiple expansions of eigen and associated vectors of such operator pencils are closely connected with the research of differential operator equation with the boundary conditions},
year = {2015}
}
TY - JOUR T1 - Spectral Theory 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.2015040401.15 DO - 10.11648/j.pamj.s.2015040401.15 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 22 EP - 26 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.s.2015040401.15 AB - The theorem on possibility of multiple summation of the series on eigen and associated vectors of the operator pencil in the Hilbert space is proved. Research of multiple completeness and multiple expansions of eigen and associated vectors of such operator pencils are closely connected with the research of differential operator equation with the boundary conditions VL - 4 IS - 4-1 ER -
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