For the multiparameter system of operators in three parameters the conditions of the existence of multiple basis of eigen and associated vectors in finite dimensional space is proved. The proof of this fact uses essentially the notion of the Resultant of two operator pencils, acting in, generally speaking, in different Hilbert spaces and the criterion of existence of common eigenvalues of several operator pencils, acting in Hilbert spaces.
| 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.2015040401.12 |
| Page(s) | 5-10 |
| 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 |
Eigen and Associated Vectors, Finite Dimensional Space, Multiparameter System of Operators, Nonlinear Algebraic System of Equations, Resultant-Operator of Two Pencils
| [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] | Dzhabarzadeh R. M., Salmanova G. H. About solutions of algebraic systems, Proceeding of IMM of NAS of Azerbaijan, 2010, vol. XXX(XLI), pp.43-48 |
| [5] | Dzhabarzadeh R. M. On existence of common eigen value of some operator-bundles, that depends polynomial on parameter. Baku. International Topology conference, 3-9 oct., 1987, Tez. 2, Baku, 1987, p.93. |
| [6] | Dzhabarzadeh R. M. On solutions of nonlinear algebraic systems with two variables. Pure and Applied Mathematics Journal, vol. 2, No. 1, pp. 32-37, 2013 |
| [7] | Dzhabarzadeh R M. Nonlinear algebraic equations Lambert Academic Publishing, 2013, p. 101 (in Russian) |
| [8] | Dzhabarzadeh R. M. Spectral theory of two parameter system in finite-dimensional space. Transactions of NAS of Azerbaijan, v. 3-4 1998, p.12-18 |
| [9] | Dzhabarzadeh R.M. Spectral theory of multiparameter system of operators in Hilbert space, Transactions of NAS of Azerbaijan, 1-2, 1999, 33-40. |
| [10] | Dzhabarzadeh R.M. Nonlinear algebraic system with three unknowns variables. International Journal of Research Engineering and Science (IJRES), www.ijres.org, Volume2, Issue 6,14 June, 2014, pp 54-59 |
| [11] | Balinskii A.I (Балинский) Generation of notions of Bezutiant and Resultant DAN of Ukr. SSR, ser.ph.-math and tech. of sciences, 1980,2. (in Russian). |
| [12] | Keldish M .V. On completeness of eigen functions of some classes of linear nonselfadjoint operators .Successes of Mathematical Sciences (УМН), 1971, v.27, issue.4, pp..15-47,(in Russian) |
| [13] | Khayniq (Хайниг Г). Abstract analog of Resultant for two polynomial bundles Functional analyses and its applications, 1977, 2,no. 3, p.94-95(in Russian) |
APA Style
Rakhshanda Dzhabarzadeh, Kamilla Alimardanova. (2015). Multiparameter Operator Systems with Three Parameters. Pure and Applied Mathematics Journal, 4(4-1), 5-10. https://doi.org/10.11648/j.pamj.s.2015040401.12
ACS Style
Rakhshanda Dzhabarzadeh; Kamilla Alimardanova. Multiparameter Operator Systems with Three Parameters. Pure Appl. Math. J. 2015, 4(4-1), 5-10. doi: 10.11648/j.pamj.s.2015040401.12
AMA Style
Rakhshanda Dzhabarzadeh, Kamilla Alimardanova. Multiparameter Operator Systems with Three Parameters. Pure Appl Math J. 2015;4(4-1):5-10. doi: 10.11648/j.pamj.s.2015040401.12
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.pamj.s.2015040401.12,
author = {Rakhshanda Dzhabarzadeh and Kamilla Alimardanova},
title = {Multiparameter Operator Systems with Three Parameters},
journal = {Pure and Applied Mathematics Journal},
volume = {4},
number = {4-1},
pages = {5-10},
doi = {10.11648/j.pamj.s.2015040401.12},
url = {https://doi.org/10.11648/j.pamj.s.2015040401.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040401.12},
abstract = {For the multiparameter system of operators in three parameters the conditions of the existence of multiple basis of eigen and associated vectors in finite dimensional space is proved. The proof of this fact uses essentially the notion of the Resultant of two operator pencils, acting in, generally speaking, in different Hilbert spaces and the criterion of existence of common eigenvalues of several operator pencils, acting in Hilbert spaces.},
year = {2015}
}
TY - JOUR T1 - Multiparameter Operator Systems with Three Parameters AU - Rakhshanda Dzhabarzadeh AU - Kamilla Alimardanova Y1 - 2015/05/12 PY - 2015 N1 - https://doi.org/10.11648/j.pamj.s.2015040401.12 DO - 10.11648/j.pamj.s.2015040401.12 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 5 EP - 10 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.s.2015040401.12 AB - For the multiparameter system of operators in three parameters the conditions of the existence of multiple basis of eigen and associated vectors in finite dimensional space is proved. The proof of this fact uses essentially the notion of the Resultant of two operator pencils, acting in, generally speaking, in different Hilbert spaces and the criterion of existence of common eigenvalues of several operator pencils, acting in Hilbert spaces. VL - 4 IS - 4-1 ER -
Email: