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On Existence of Eigen Values of Several Operator Bundles with Two Parameters

Received: 19 April 2015     Accepted: 14 May 2015     Published: 21 August 2015
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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

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

Keywords

Operator, Space, Resultant, Criterion, Eigenvector, Bundle

References
[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. 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.
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  • 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

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    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

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    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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  • @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}
    }
    

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    AU  - Makhmudova Malaka Gasan
    AU  - Sultanova Elnara Bayram
    Y1  - 2015/08/21
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    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
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Author Information
  • Department of Higher Mathematics, Baku State University, Baku, Azerbaijan

  • Department of Applied Mathematics, Baku State University, Baku, Azerbaijan

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