Multiparameter System of Operators with Two Parameters in Finite Dimensional Spaces
Pure and Applied Mathematics Journal
Volume 4, Issue 4-1, August 2015, Pages: 1-4
Received: Feb. 25, 2015;
Accepted: Feb. 27, 2015;
Published: May 12, 2015
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Rakhshanda Dzhabarzadeh, Department of functional analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku
Afet Jabrailova, Department of functional analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku
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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.
Multiparameter, Spectrum, Operator, Space, Eigenvector
To cite this article
Multiparameter System of Operators with Two Parameters in Finite Dimensional Spaces, Pure and Applied Mathematics Journal. Special Issue: Spectral Theory of Multiparameter Operator Pencils and Its Applications.
Vol. 4, No. 4-1,
2015, pp. 1-4.
Atkinson F.V. Multiparameter spectral theory. Bull.Amer. Math.Soc.1968, 74, 1-27.
Browne P.J. Multiparameter spectral theory. Indiana Univ. Math. J,24, 3, 1974
Sleeman B.D. Multiparameter spectral theory in Hilbert space. Pitnam Press, London, 1978, p.118.
Dzhabarzadeh R.M. Spectral theory of two parameter system in finite-dimensional space. Transactions of NAS Azerbaijan, v. 3-4 1998, p.12-18
Dzhabarzadeh R.M. Spectral theory of multiparameter system of operators in Hilbert space, Transactions of NAS of Azerbaijan, 1-2, 1999, 33-41
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).
Khayniq (Хайниг Г). Abstract analog of Resultant for two polynomial bundles Functional analyses and its applications, 1977, 2 , no. 3, p.94-95
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
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)