Research Methods of Multiparameter System in Hilbert Spaces

Rakhshanda Dzhabarzadeh

doi:doi:10.11648/j.pamj.s.2015040401.18

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Research Methods of Multiparameter System in Hilbert Spaces

Rakhshanda Dzhabarzadeh

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 4-1)

Received: 9 May 2015 Accepted: 19 May 2015 Published: 24 August 2015

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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 system in Hilbert space. These approaches solve questions of completeness, multiple completeness, the basis and a multiple basis property of eigen and associated vectors of multiparameter systems with a complex dependence on the parameters

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.2015040401.18
Page(s)	38-44
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

Method, Atkinson, Multiparameter Systems, Basis, Complete

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]	Mors F.V..Feshbakh Q. The methods of theoretical physics. M.,IL,1958,pp.930
[4]	Roach G.F.Classification and reductionof general multiparameter problems. Univ,Gottigen, NAM,Bericht, 12,1974
[5]	Sleeman B.D. Klein oscillatory theorems for multiparameter eigenvalue prin.ord. diff. equat. Nieuw Archif voor Wiskunde 3 XXVII,1979,341-362
[6]	Allakhverdiev J.E., Dzhabarzadeh R.M. Abstract separation of variables.DAN SSSR,1988,t.300 , 2, pp. 269=271
[7]	Faierman M. The expansiontheoremin multiparameter spectral theory. Lect. Notes Math.1974,415,pp.137-142
[8]	Dzhabarzadeh R.M. Spectral theory of two parameter system in finite-dimensional space. Transactions of NAS Azerbaijan, v. 3-4 1998, p.12-18
[9]	Dzhabarzadeh R.M. Spectral theory of multiparameter system of operators in Hilbert space, Transactions of NAS of Azerbaijan, 1-2, 1999, 33-40.
[10]	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).
[11]	Khayniq (Хайниг Г). Abstract analog of Resultant for two polynomial bundles.Functional analysis and its applications,1977, 2 , no. 3, p.94-95,
[12]	Dzhabarzadeh R.M. On existence of common eigen value of some operator-bundles, that depends polynomial on parameter. Baku.International Topology conference, 3-9 оct., 1987, Теz., 2, Baku, 1987, p.93
[13]	Dzhabarzadeh R.M., Salmanova G.H. About solutions of algebraic systems. Proceedings of NAS Azerbaijan, XXXIII (41), 2010, pp.43-48
[14]	Dzhabarzadeh R.M, Salmanova G.H. Multtiparameter system of operators, not linearly depending on parameters. American Journal of Mathematics and Mathematical Sciences.- 2012, vol.1, No.2.- p.39-45.
[15]	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
[16]	Rakhshanda Dzhabarzadeh Multiparameter spectral theory.Lambert Academic Publishing, 2012, pp. 184 .
[17]	Prugovecku E.Quantum Mechanics in Hilbert bspace.Academic Press, New York, London,1971.
[18]	Dzhabarzadeh R.M. Structure of eigen and associated vectors of not selfadjoint multiparameter system in the Hilbert spaces. Proc.of IMM of NAS of Azerb.- 2011, vol.XXXV (XLIII).- p.11- 21

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Rakhshanda Dzhabarzadeh. (2015). Research Methods of Multiparameter System in Hilbert Spaces. Pure and Applied Mathematics Journal, 4(4-1), 38-44. https://doi.org/10.11648/j.pamj.s.2015040401.18

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Rakhshanda Dzhabarzadeh. Research Methods of Multiparameter System in Hilbert Spaces. Pure Appl. Math. J. 2015, 4(4-1), 38-44. doi: 10.11648/j.pamj.s.2015040401.18

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AMA Style

Rakhshanda Dzhabarzadeh. Research Methods of Multiparameter System in Hilbert Spaces. Pure Appl Math J. 2015;4(4-1):38-44. doi: 10.11648/j.pamj.s.2015040401.18

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@article{10.11648/j.pamj.s.2015040401.18,
  author = {Rakhshanda Dzhabarzadeh},
  title = {Research Methods of Multiparameter System in Hilbert Spaces},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {4-1},
  pages = {38-44},
  doi = {10.11648/j.pamj.s.2015040401.18},
  url = {https://doi.org/10.11648/j.pamj.s.2015040401.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040401.18},
  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 system in Hilbert space. These approaches solve questions of completeness, multiple completeness, the basis and a multiple basis property of eigen and associated vectors of multiparameter systems with a complex dependence on the parameters},
 year = {2015}
}

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TY  - JOUR
T1  - Research Methods of Multiparameter System in Hilbert Spaces
AU  - Rakhshanda Dzhabarzadeh
Y1  - 2015/08/24
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.s.2015040401.18
DO  - 10.11648/j.pamj.s.2015040401.18
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 38
EP  - 44
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.s.2015040401.18
AB  - 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 system in Hilbert space. These approaches solve questions of completeness, multiple completeness, the basis and a multiple basis property of eigen and associated vectors of multiparameter systems with a complex dependence on the parameters
VL  - 4
IS  - 4-1
ER  -

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Author Information

Rakhshanda Dzhabarzadeh

Department of Functional Analysis of Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan

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Rakhshanda Dzhabarzadeh. (2015). Research Methods of Multiparameter System in Hilbert Spaces. Pure and Applied Mathematics Journal, 4(4-1), 38-44. https://doi.org/10.11648/j.pamj.s.2015040401.18

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ACS Style

Rakhshanda Dzhabarzadeh. Research Methods of Multiparameter System in Hilbert Spaces. Pure Appl. Math. J. 2015, 4(4-1), 38-44. doi: 10.11648/j.pamj.s.2015040401.18

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AMA Style

Rakhshanda Dzhabarzadeh. Research Methods of Multiparameter System in Hilbert Spaces. Pure Appl Math J. 2015;4(4-1):38-44. doi: 10.11648/j.pamj.s.2015040401.18

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@article{10.11648/j.pamj.s.2015040401.18,
  author = {Rakhshanda Dzhabarzadeh},
  title = {Research Methods of Multiparameter System in Hilbert Spaces},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {4-1},
  pages = {38-44},
  doi = {10.11648/j.pamj.s.2015040401.18},
  url = {https://doi.org/10.11648/j.pamj.s.2015040401.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2015040401.18},
  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 system in Hilbert space. These approaches solve questions of completeness, multiple completeness, the basis and a multiple basis property of eigen and associated vectors of multiparameter systems with a complex dependence on the parameters},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Research Methods of Multiparameter System in Hilbert Spaces
AU  - Rakhshanda Dzhabarzadeh
Y1  - 2015/08/24
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.s.2015040401.18
DO  - 10.11648/j.pamj.s.2015040401.18
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 38
EP  - 44
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.s.2015040401.18
AB  - 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 system in Hilbert space. These approaches solve questions of completeness, multiple completeness, the basis and a multiple basis property of eigen and associated vectors of multiparameter systems with a complex dependence on the parameters
VL  - 4
IS  - 4-1
ER  -

Copy | Download