The authors have proved the existence of the multiple basis on the eigen and associated elements of the two parameter system of operators in finite dimensional spaces. The proof uses the notion of the abstract analog of resultant of two operator pencils, acting, generally speaking, in different Hilbert spaces. In this paper necessary and sufficient conditions of the existence of multiple completeness of the eigen and associated vectors of two parameter system of operators in finite dimensional Hilbert space is given.
| 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.2015040401.11 |
| Page(s) | 1-4 |
| 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 |
Multiparameter, Spectrum, Operator, Space, Eigenvector
| [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. Spectral theory of two parameter system in finite-dimensional space. Transactions of NAS Azerbaijan, v. 3-4 1998, p.12-18 |
| [5] | Dzhabarzadeh R.M. Spectral theory of multiparameter system of operators in Hilbert space, Transactions of NAS of Azerbaijan, 1-2, 1999, 33-41 |
| [6] | 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). |
| [7] | Khayniq (Хайниг Г). Abstract analog of Resultant for two polynomial bundles Functional analyses and its applications, 1977, 2 , no. 3, p.94-95 |
| [8] | Dzhabarzadeh R.M. On solutions of nonlinear algebraic systems with two variables. Pure and Applied Mathematics Journal, vol. 2, No. 1, pp. 31-37, 2013 |
| [9] | 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) |
APA Style
Rakhshanda Dzhabarzadeh, Afet Jabrailova. (2015). Multiparameter System of Operators with Two Parameters in Finite Dimensional Spaces. Pure and Applied Mathematics Journal, 4(4-1), 1-4. https://doi.org/10.11648/j.pamj.s.2015040401.11
ACS Style
Rakhshanda Dzhabarzadeh; Afet Jabrailova. Multiparameter System of Operators with Two Parameters in Finite Dimensional Spaces. Pure Appl. Math. J. 2015, 4(4-1), 1-4. doi: 10.11648/j.pamj.s.2015040401.11
AMA Style
Rakhshanda Dzhabarzadeh, Afet Jabrailova. Multiparameter System of Operators with Two Parameters in Finite Dimensional Spaces. Pure Appl Math J. 2015;4(4-1):1-4. doi: 10.11648/j.pamj.s.2015040401.11
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Download@article{10.11648/j.pamj.s.2015040401.11,
author = {Rakhshanda Dzhabarzadeh and Afet Jabrailova},
title = {Multiparameter System of Operators with Two Parameters in Finite Dimensional Spaces},
journal = {Pure and Applied Mathematics Journal},
volume = {4},
number = {4-1},
pages = {1-4},
doi = {10.11648/j.pamj.s.2015040401.11},
url = {https://doi.org/10.11648/j.pamj.s.2015040401.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040401.11},
abstract = {The authors have proved the existence of the multiple basis on the eigen and associated elements of the two parameter system of operators in finite dimensional spaces. The proof uses the notion of the abstract analog of resultant of two operator pencils, acting, generally speaking, in different Hilbert spaces. In this paper necessary and sufficient conditions of the existence of multiple completeness of the eigen and associated vectors of two parameter system of operators in finite dimensional Hilbert space is given.},
year = {2015}
}
TY - JOUR T1 - Multiparameter System of Operators with Two Parameters in Finite Dimensional Spaces AU - Rakhshanda Dzhabarzadeh AU - Afet Jabrailova Y1 - 2015/05/12 PY - 2015 N1 - https://doi.org/10.11648/j.pamj.s.2015040401.11 DO - 10.11648/j.pamj.s.2015040401.11 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 1 EP - 4 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.s.2015040401.11 AB - The authors have proved the existence of the multiple basis on the eigen and associated elements of the two parameter system of operators in finite dimensional spaces. The proof uses the notion of the abstract analog of resultant of two operator pencils, acting, generally speaking, in different Hilbert spaces. In this paper necessary and sufficient conditions of the existence of multiple completeness of the eigen and associated vectors of two parameter system of operators in finite dimensional Hilbert space is given. VL - 4 IS - 4-1 ER -
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