Pure and Applied Mathematics Journal

Volume 4, Issue 4, August 2015

  • Multiparameter System of Operators with Two Parameters in Finite Dimensional Spaces

    Rakhshanda Dzhabarzadeh, Afet Jabrailova

    Issue: Volume 4, Issue 4-1, August 2015
    Pages: 1-4
    Received: 25 February 2015
    Accepted: 27 February 2015
    Published: 12 May 2015
    Downloads:
    Views:
    Abstract: The authors have proved the existence of the multiple basis on the eigen and associated elements of the two parameter system of operators in finite dimensional spaces. The proof uses the notion of the abstract analog of resultant of two operator pencils, acting, generally speaking, in different Hilbert spaces. In this paper necessary and sufficient... Show More
  • Multiparameter Operator Systems with Three Parameters

    Rakhshanda Dzhabarzadeh, Kamilla Alimardanova

    Issue: Volume 4, Issue 4-1, August 2015
    Pages: 5-10
    Received: 25 February 2015
    Accepted: 27 February 2015
    Published: 12 May 2015
    Downloads:
    Views:
    Abstract: For the multiparameter system of operators in three parameters the conditions of the existence of multiple basis of eigen and associated vectors in finite dimensional space is proved. The proof of this fact uses essentially the notion of the Resultant of two operator pencils, acting in, generally speaking, in different Hilbert spaces and the criter... Show More
  • Criterion of Existence of Eigen Values of Linear Multiparameter Systems

    Rakhshanda Dzhabarzadeh, Elnara Sultanova

    Issue: Volume 4, Issue 4-1, August 2015
    Pages: 11-15
    Received: 23 March 2015
    Accepted: 10 April 2015
    Published: 12 May 2015
    Downloads:
    Views:
    Abstract: It is considered the linear multiparameter system of operators when the number of equations may be more than the number of parameters. For such multiparameter systems the authors have proved the criterion of existence of eigen values. Under certain conditions, the authors a have proved that all components of the eigen values of the considered multi... Show More
  • On Existence of Eigen Values of Several Operator Bundles with Two Parameters

    Makhmudova Malaka Gasan, Sultanova Elnara Bayram

    Issue: Volume 4, Issue 4-1, August 2015
    Pages: 16-21
    Received: 19 April 2015
    Accepted: 14 May 2015
    Published: 21 August 2015
    Downloads:
    Views:
    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 ... Show More
  • Spectral Theory of Operator Pencils in the Hilbert Spaces

    Rakhshanda Dzhabarzadeh

    Issue: Volume 4, Issue 4-1, August 2015
    Pages: 22-26
    Received: 29 April 2015
    Accepted: 14 May 2015
    Published: 21 August 2015
    Downloads:
    Views:
    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 bo... Show More
  • On Multiple Bases of Eigen and Associated Vectors of Operator Pencils in the Hilbert Spaces

    Rakhshanda Dzhabarzadeh

    Issue: Volume 4, Issue 4-1, August 2015
    Pages: 27-32
    Received: 4 May 2015
    Accepted: 19 May 2015
    Published: 21 August 2015
    Downloads:
    Views:
    Abstract: It is proved the theorem about of multiple basis of eigen and associated vectors of the operator pencil, non-linear depending on parameter in the Hilbert space. This work is the generalization of existing results on the multiple completeness of the eigen and associated vectors of polynomial pencils, rationally depending on parameters. At the proof ... Show More
  • Spectral Problems of Two-Parameter System of Operators

    Rakhshanda Dzhabarzadeh

    Issue: Volume 4, Issue 4-1, August 2015
    Pages: 33-37
    Received: 4 May 2015
    Accepted: 19 May 2015
    Published: 21 August 2015
    Downloads:
    Views:
    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... Show More
  • Research Methods of Multiparameter System in Hilbert Spaces

    Rakhshanda Dzhabarzadeh

    Issue: Volume 4, Issue 4-1, August 2015
    Pages: 38-44
    Received: 9 May 2015
    Accepted: 19 May 2015
    Published: 24 August 2015
    Downloads:
    Views:
    Abstract: The work is devoted to the presentation of the methods, available in the literature, of the study of multiparameter spectral problems in Hilbert space. In particular, the method of Atkinson and his followers for a purely self-adjoint multiparameter systems and methods proposed by the author for the study, in general, non- selfadjoint multiparameter... Show More