| Peer-Reviewed

Spectral Theory of Operator Pencils in the Hilbert Spaces

Received: 29 April 2015     Accepted: 14 May 2015     Published: 21 August 2015
Views:       Downloads:
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

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.2015040401.15
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), 2015. 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.
Cite This Article
  • APA Style

    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

    Copy | Download

    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

    Copy | Download

    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

    Copy | Download

  • @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://article.sciencepublishinggroup.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}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Spectral Theory of Operator Pencils in the Hilbert Spaces
    AU  - Rakhshanda Dzhabarzadeh
    Y1  - 2015/08/21
    PY  - 2015
    N1  - https://doi.org/10.11648/j.pamj.s.2015040401.15
    DO  - 10.11648/j.pamj.s.2015040401.15
    T2  - Pure and Applied Mathematics Journal
    JF  - Pure and Applied Mathematics Journal
    JO  - Pure and Applied Mathematics Journal
    SP  - 22
    EP  - 26
    PB  - Science Publishing Group
    SN  - 2326-9812
    UR  - https://doi.org/10.11648/j.pamj.s.2015040401.15
    AB  - 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
    VL  - 4
    IS  - 4-1
    ER  - 

    Copy | Download

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

  • Sections