Pure and Applied Mathematics Journal

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Spectral Theory of Operator Pencils in the Hilbert Spaces

Received: 29 April 2015    Accepted: 14 May 2015    Published: 21 August 2015
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Abstract

The theorem on possibility of multiple summation of the series on eigen and associated vectors of the operator pencil in the Hilbert space is proved. Research of multiple completeness and multiple expansions of eigen and associated vectors of such operator pencils are closely connected with the research of differential operator equation with the boundary conditions

DOI 10.11648/j.pamj.s.2015040401.15
Published in Pure and Applied Mathematics Journal (Volume 4, Issue 4-1, August 2015)

This article belongs to the Special Issue Spectral Theory of Multiparameter Operator Pencils and Its Applications

Page(s) 22-26
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

Keywords

Operator Pencil, Residue, Completely Continuous, Multiple

References
[1] Keldysh M.V. About completeness of eigen functions of some class linear non-selfadjoint operators. Journal Success of Mathematical Science .1971, т.27, issue.4,p.15-47
[2] Dzhabarzadeh R.M. On expansions series on eigen and associated vectors of operator pencils Journal: Scientific notes of Azerb.State University,1964, №3,pp.75-81.
[3] Vizitei V.N., Markus A.S. On convergence of multiple expansions on the system of eigen and associated vectors of polynomial pencils /Mathematical collection,1965,т.66, №2, pp..287-320
[4] Gokhberg I.Ts., Kreyn M.Q. Introduction to the theory of linear non-selfadjoint operators in the Hilbert space.Moscow,1964, pp 1-433.
[5] Allakhverdiev J.E., Dzhabarzadeh R. M. // Spectral theory of operator pencil in the Hilbert space. ДAN of Azerbaijan, 2011, т.LXVII, № 4., pр.3-10.
[6] Allakhverdiev J.E.,Dzhabarzadeh R.M. Оn summation of multiple series on eigen and associated vectors of operator pencils by Abel’s method. ДАN Аz SSR, 1979,т.35, № 7,p 19-23.
[7] Lidskii V.B.. About summation of the series on the general vectors of the non-selfadjoint operators. Proceeding of Moscow Scientific Society, t.11, 1962.
[8] Radzievskii Q.V.Multiple completeness of root vectors of Keldysh’s operator pencil, disturbing by analytical operatorfunction.DAN USSR,ser.A,1976,,7,pp.597-600.
[9] Dzhabarzadeh R. M. To the spectral theory of polynomial pencils.Proceedinfg of Oryol State Universitety Russia ,2006,t.1,pp.161-165.
Author Information
  • Department of functional analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan

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    Rakhshanda Dzhabarzadeh. (2015). Spectral Theory of Operator Pencils in the Hilbert Spaces. Pure and Applied Mathematics Journal, 4(4-1), 22-26. https://doi.org/10.11648/j.pamj.s.2015040401.15

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    ACS Style

    Rakhshanda Dzhabarzadeh. Spectral Theory of Operator Pencils in the Hilbert Spaces. Pure Appl. Math. J. 2015, 4(4-1), 22-26. doi: 10.11648/j.pamj.s.2015040401.15

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    AMA Style

    Rakhshanda Dzhabarzadeh. Spectral Theory of Operator Pencils in the Hilbert Spaces. Pure Appl Math J. 2015;4(4-1):22-26. doi: 10.11648/j.pamj.s.2015040401.15

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  • @article{10.11648/j.pamj.s.2015040401.15,
      author = {Rakhshanda Dzhabarzadeh},
      title = {Spectral Theory of Operator Pencils in the Hilbert Spaces},
      journal = {Pure and Applied Mathematics Journal},
      volume = {4},
      number = {4-1},
      pages = {22-26},
      doi = {10.11648/j.pamj.s.2015040401.15},
      url = {https://doi.org/10.11648/j.pamj.s.2015040401.15},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.pamj.s.2015040401.15},
      abstract = {The theorem on possibility of multiple summation of the series on eigen and associated vectors of the operator pencil in the Hilbert space is proved. Research of multiple completeness and multiple expansions of eigen and associated vectors of such operator pencils are closely connected with the research of differential operator equation with the boundary conditions},
     year = {2015}
    }
    

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