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Spectral Problems of Two-Parameter System of Operators

Received: 4 May 2015     Accepted: 19 May 2015     Published: 21 August 2015
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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

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

Keywords

Multiparameter, Spectrum, Operator, Space, Eigenvector

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] 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)
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  • 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

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    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

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    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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  • @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}
    }
    

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    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
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    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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Author Information
  • Department of functional analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan

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