For the several operator bundles with two parameters when the number of equation is greater than the number of parameters in the Hilbert spaces is given the criterion of existence of the common point of spectra. In the special case the common point of spectra is the common eigen value. In the proof of the theorem the authors use the results of the spectral theory of multiparameter systems
| 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.2015040401.14 |
| Page(s) | 16-21 |
| 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, Space, Resultant, Criterion, Eigenvector, Bundle
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| [3] | Sleeman B.D. Multiparameter spectral theory in Hilbert space. Pitnam Press, London, 1978, p.118. |
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| [5] | Dzhabarzadeh R.M. Spectral theory of two parameter system in finite-dimensional space. Transactions of NAS Azerbaijan, v. 3-4 1998, p.12-18. |
| [6] | Dzhabarzadeh R.M. Spectral theory of multiparameter system of operators in Hilbert space, Transactions of NAS of Azerbaijan, 1-2, 1999, 33-40. |
| [7] | Dzhabarzadeh R.M. Multiparameter spectral theory. Lambert Academic Publishing, 2012, pp. 184 (in Russian). |
| [8] | Dzhabarzadeh R.M. Nonlinear algebraic systems. Lambert Academic Publishing, 2013, pp. 101(in Russian). |
| [9] | Dzhabarzadeh R.M. About Solutions of Nonlinear Algebraic System with Two Variables. Pure and Applied Mathematics Journal,vol. 2, No. 1, pp. 32-37, 2013. |
| [10] | Dzhabarzadeh R.M. On existence of common eigenvalues of some operator bundles polynomial depending on parameter. Baku, International Conference on Topoloji. 3-9 0ctober 1987.Tez.p-.2, Baku,p,93. |
| [11] | Khayniq Q. Abstract analog of Resultant for two polynomial bundles Functional analyses and its applications, 1977, 2,no. 3, p.94-95. |
| [12] | Dzhabarzadeh R.M. Structure of eigen and associated vectors of not adjoint multiparameter system in the Hilbert space. Proc.of IMM of NAS of Azerb.- 2011, vol.XXXV (XLIII).- p.11- 21. |
APA Style
Makhmudova Malaka Gasan, Sultanova Elnara Bayram. (2015). On Existence of Eigen Values of Several Operator Bundles with Two Parameters. Pure and Applied Mathematics Journal, 4(4-1), 16-21. https://doi.org/10.11648/j.pamj.s.2015040401.14
ACS Style
Makhmudova Malaka Gasan; Sultanova Elnara Bayram. On Existence of Eigen Values of Several Operator Bundles with Two Parameters. Pure Appl. Math. J. 2015, 4(4-1), 16-21. doi: 10.11648/j.pamj.s.2015040401.14
AMA Style
Makhmudova Malaka Gasan, Sultanova Elnara Bayram. On Existence of Eigen Values of Several Operator Bundles with Two Parameters. Pure Appl Math J. 2015;4(4-1):16-21. doi: 10.11648/j.pamj.s.2015040401.14
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Download@article{10.11648/j.pamj.s.2015040401.14,
author = {Makhmudova Malaka Gasan and Sultanova Elnara Bayram},
title = {On Existence of Eigen Values of Several Operator Bundles with Two Parameters},
journal = {Pure and Applied Mathematics Journal},
volume = {4},
number = {4-1},
pages = {16-21},
doi = {10.11648/j.pamj.s.2015040401.14},
url = {https://doi.org/10.11648/j.pamj.s.2015040401.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040401.14},
abstract = {For the several operator bundles with two parameters when the number of equation is greater than the number of parameters in the Hilbert spaces is given the criterion of existence of the common point of spectra. In the special case the common point of spectra is the common eigen value. In the proof of the theorem the authors use the results of the spectral theory of multiparameter systems},
year = {2015}
}
TY - JOUR T1 - On Existence of Eigen Values of Several Operator Bundles with Two Parameters AU - Makhmudova Malaka Gasan AU - Sultanova Elnara Bayram Y1 - 2015/08/21 PY - 2015 N1 - https://doi.org/10.11648/j.pamj.s.2015040401.14 DO - 10.11648/j.pamj.s.2015040401.14 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 16 EP - 21 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.s.2015040401.14 AB - For the several operator bundles with two parameters when the number of equation is greater than the number of parameters in the Hilbert spaces is given the criterion of existence of the common point of spectra. In the special case the common point of spectra is the common eigen value. In the proof of the theorem the authors use the results of the spectral theory of multiparameter systems VL - 4 IS - 4-1 ER -
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