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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
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 conditions of the existence of multiple completeness of the eigen and associated vectors of two parameter system of operators in finite dimensional Hilbert space is given.
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...
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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
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 criterion of existence of common eigenvalues of several operator pencils, acting in Hilbert spaces.
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...
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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
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 multiparameter systems are real numbers.
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...
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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
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 spectral theory of multiparameter systems
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 ...
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Spectral Theory of Operator Pencils in the Hilbert Spaces
Issue:
Volume 4, Issue 4-1, August 2015
Pages:
22-26
Received:
29 April 2015
Accepted:
14 May 2015
Published:
21 August 2015
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
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...
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On Multiple Bases of Eigen and Associated Vectors of Operator Pencils in the Hilbert Spaces
Issue:
Volume 4, Issue 4-1, August 2015
Pages:
27-32
Received:
4 May 2015
Accepted:
19 May 2015
Published:
21 August 2015
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 the author uses the methods of spectral theory of operators
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 ...
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Spectral Problems of Two-Parameter System of Operators
Issue:
Volume 4, Issue 4-1, August 2015
Pages:
33-37
Received:
4 May 2015
Accepted:
19 May 2015
Published:
21 August 2015
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
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...
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Research Methods of Multiparameter System in Hilbert Spaces
Issue:
Volume 4, Issue 4-1, August 2015
Pages:
38-44
Received:
9 May 2015
Accepted:
19 May 2015
Published:
24 August 2015
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
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...
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