It is considered the linear multiparameter system of operators when the number of equations may be more than the number of parameters. For such multiparameter systems the authors have proved the criterion of existence of eigen values. Under certain conditions, the authors a have proved that all components of the eigen values of the considered multiparameter systems are real numbers.
| 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.2015040401.13 |
| Page(s) | 11-15 |
| 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, Parameter, Eigenvalue, System, Multiparameter
| [1] | Atkinson F.V. Multiparameter spectral theory. Bull.Amer.Math.Soc.1968, 74, 1-27. |
| [2] | Browne P.J. Multiparameter spectral theory. Indiana Univ. Math. J,24, 3, 1974. |
| [3] | Sleeman B.D. Multiparameter spectral theory in Hilbert space. Pitnam Press, London, 1978, p.118. |
| [4] | Balinskii A.I Generation of notions of Bezutiant and Resultant DAN of Ukr. SSR, ser.ph.-math and tech. of sciences,1980,2. (in Russian). |
| [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. Common solutions of several polinomials in one or more variables. FEN-nauka, Russia ,1(40),pp.6-12 2015,Sayt 134786. |
| [10] | 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. |
| [11] | 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. |
| [12] | Khayniq (Хайниг Г) .Abstract analog of Resultant for two polynomial bundles Functional analyses and its applications, 1977, 2,no. 3, p.94-95. |
APA Style
Rakhshanda Dzhabarzadeh, Elnara Sultanova. (2015). Criterion of Existence of Eigen Values of Linear Multiparameter Systems. Pure and Applied Mathematics Journal, 4(4-1), 11-15. https://doi.org/10.11648/j.pamj.s.2015040401.13
ACS Style
Rakhshanda Dzhabarzadeh; Elnara Sultanova. Criterion of Existence of Eigen Values of Linear Multiparameter Systems. Pure Appl. Math. J. 2015, 4(4-1), 11-15. doi: 10.11648/j.pamj.s.2015040401.13
AMA Style
Rakhshanda Dzhabarzadeh, Elnara Sultanova. Criterion of Existence of Eigen Values of Linear Multiparameter Systems. Pure Appl Math J. 2015;4(4-1):11-15. doi: 10.11648/j.pamj.s.2015040401.13
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.pamj.s.2015040401.13,
author = {Rakhshanda Dzhabarzadeh and Elnara Sultanova},
title = {Criterion of Existence of Eigen Values of Linear Multiparameter Systems},
journal = {Pure and Applied Mathematics Journal},
volume = {4},
number = {4-1},
pages = {11-15},
doi = {10.11648/j.pamj.s.2015040401.13},
url = {https://doi.org/10.11648/j.pamj.s.2015040401.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040401.13},
abstract = {It is considered the linear multiparameter system of operators when the number of equations may be more than the number of parameters. For such multiparameter systems the authors have proved the criterion of existence of eigen values. Under certain conditions, the authors a have proved that all components of the eigen values of the considered multiparameter systems are real numbers.},
year = {2015}
}
TY - JOUR T1 - Criterion of Existence of Eigen Values of Linear Multiparameter Systems AU - Rakhshanda Dzhabarzadeh AU - Elnara Sultanova Y1 - 2015/05/12 PY - 2015 N1 - https://doi.org/10.11648/j.pamj.s.2015040401.13 DO - 10.11648/j.pamj.s.2015040401.13 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 11 EP - 15 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.s.2015040401.13 AB - It is considered the linear multiparameter system of operators when the number of equations may be more than the number of parameters. For such multiparameter systems the authors have proved the criterion of existence of eigen values. Under certain conditions, the authors a have proved that all components of the eigen values of the considered multiparameter systems are real numbers. VL - 4 IS - 4-1 ER -
Email: