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Spectral Problems of Multiparameter System of Operators with Two Parameters
Current Issue
Volume 3, 2015
Issue 2 (April)
Pages: 34-38   |   Vol. 3, No. 2, April 2015   |   Follow on         
Paper in PDF Downloads: 24   Since Aug. 28, 2015 Views: 2101   Since Aug. 28, 2015
Authors
[1]
Rakhshanda Dzhabarzadeh, Department of Functional Analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.
[2]
Afet Jabrailova, Department of Functional Analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.
Abstract
In this paper sufficient conditions of the existence of multiple completeness of the eigen and associated vectors of two parameter system of operators in the Hilbert space are given. In the special case when the spaces have the finite dimensions these sufficient conditions are also necessary. The operators in the multiparameter system are not necessarily selfadjoint. The method, used in the work, allows to consider a system with a complex dependence on the parameters.The proof uses the notion of the abstract analog of resultant of two operator pencils, acting, generally speaking, in different Hilbert spaces.
Keywords
Multiparameter, Spectrum, Operator, Space, Eigenvector
Reference
[1]
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[2]
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Dzhabarzadeh R.M. Spectral theory of two parameter system in finite-dimensional space. Transactions of NAS Azerbaijan, v. 3-4 1998, p.12-18.
[5]
Dzhabarzadeh R.M. Spectral theory of multiparameter system of operators in Hilbert space, Transactions of NAS of Azerbaijan, 1-2, 1999, 33-41.
[6]
Balinskii A.I (Балинский) Generation of notions of Bezutiant and Resultant DAN of Ukr. SSR, ser.ph.-math and tech. of sciences, 1980, 2. (in Russian).
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[8]
Dzhabarzadeh R.M. On solutions of nonlinear algebraic systems with two variables. Pure and Applied Mathematics Journal, vol. 2, No. 1, pp. 31-37, 2013.
[9]
Keldish M .V. On completeness of eigen functions of some classes of linear nonselfadjoint operators .Successes of Mathematical Sciences (УМН), 1971, v.27, issue.4, pp.15-47 (in Russian).
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