The author has proved the existence of the multiple basis of the eigen and associated vectors of the two parameter system of operators in Hilbert spaces. The proof essentially uses the theorem of the existence of multiple basis of operator bundles and the notion of the abstract analog of resultant of two operator pencils, acting, generally speaking, in different Hilbert spaces. Considerable non-selfadjoint two parameter systems depend on both parameters in a complicated manner
| 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.2015040401.17 |
| Page(s) | 33-37 |
| 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 |
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. About expansion on eigen and associated vectors of operator pencil polynomially depending on parameters. Scientific notes of Azerbaijan State University 1964, № 3,с.75-81 |
| [6] | Dzhabarzadeh R.M.Spectral theory of multiparameter system of operators in Hilbert space, Transactions of NAS of Azerbaijan, 1-2, 1999, 33-41 |
| [7] | 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). |
| [8] | Khayniq (Хайниг Г). Abstract analog of Resultant for two polynomial bundles Functional analyses and its applications, 1977, 2 , no. 3, p.94-95 |
| [9] | 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 |
| [10] | 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. (2015). Spectral Problems of Two-Parameter System of Operators. Pure and Applied Mathematics Journal, 4(4-1), 33-37. https://doi.org/10.11648/j.pamj.s.2015040401.17
ACS Style
Rakhshanda Dzhabarzadeh. Spectral Problems of Two-Parameter System of Operators. Pure Appl. Math. J. 2015, 4(4-1), 33-37. doi: 10.11648/j.pamj.s.2015040401.17
AMA Style
Rakhshanda Dzhabarzadeh. Spectral Problems of Two-Parameter System of Operators. Pure Appl Math J. 2015;4(4-1):33-37. doi: 10.11648/j.pamj.s.2015040401.17
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Download@article{10.11648/j.pamj.s.2015040401.17,
author = {Rakhshanda Dzhabarzadeh},
title = {Spectral Problems of Two-Parameter System of Operators},
journal = {Pure and Applied Mathematics Journal},
volume = {4},
number = {4-1},
pages = {33-37},
doi = {10.11648/j.pamj.s.2015040401.17},
url = {https://doi.org/10.11648/j.pamj.s.2015040401.17},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040401.17},
abstract = {The author has proved the existence of the multiple basis of the eigen and associated vectors of the two parameter system of operators in Hilbert spaces. The proof essentially uses the theorem of the existence of multiple basis of operator bundles and the notion of the abstract analog of resultant of two operator pencils, acting, generally speaking, in different Hilbert spaces. Considerable non-selfadjoint two parameter systems depend on both parameters in a complicated manner},
year = {2015}
}
TY - JOUR T1 - Spectral Problems of Two-Parameter System of Operators AU - Rakhshanda Dzhabarzadeh Y1 - 2015/08/21 PY - 2015 N1 - https://doi.org/10.11648/j.pamj.s.2015040401.17 DO - 10.11648/j.pamj.s.2015040401.17 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 33 EP - 37 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.s.2015040401.17 AB - The author has proved the existence of the multiple basis of the eigen and associated vectors of the two parameter system of operators in Hilbert spaces. The proof essentially uses the theorem of the existence of multiple basis of operator bundles and the notion of the abstract analog of resultant of two operator pencils, acting, generally speaking, in different Hilbert spaces. Considerable non-selfadjoint two parameter systems depend on both parameters in a complicated manner VL - 4 IS - 4-1 ER -
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