Pure and Applied Mathematics Journal
Volume 4, Issue 4-1, August 2015, Pages: 5-10
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
Kamilla Alimardanova, Department of functional analysis of mathematics and Mechanics of NAS of Azerbaijan, Baku
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.
Multiparameter Operator Systems with Three Parameters, Pure and Applied Mathematics Journal. Special Issue: Spectral Theory of Multiparameter Operator Pencils and Its Applications.
Vol. 4, No. 4-1,
2015, pp. 5-10.
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., Salmanova G. H. About solutions of algebraic systems, Proceeding of IMM of NAS of Azerbaijan, 2010, vol. XXX(XLI), pp.43-48
Dzhabarzadeh R. M. On existence of common eigen value of some operator-bundles, that depends polynomial on parameter. Baku. International Topology conference, 3-9 oct., 1987, Tez. 2, Baku, 1987, p.93.
Dzhabarzadeh R. M. On solutions of nonlinear algebraic systems with two variables. Pure and Applied Mathematics Journal, vol. 2, No. 1, pp. 32-37, 2013
Dzhabarzadeh R M. Nonlinear algebraic equations Lambert Academic Publishing, 2013, p. 101 (in Russian)
Dzhabarzadeh R. M. Spectral theory of two parameter system in finite-dimensional space. Transactions of NAS of 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, 33-40.
Dzhabarzadeh R.M. Nonlinear algebraic system with three unknowns variables. International Journal of Research Engineering and Science (IJRES), www.ijres.org, Volume2, Issue 6,14 June, 2014, pp 54-59
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).
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)
Khayniq (Хайниг Г). Abstract analog of Resultant for two polynomial bundles Functional analyses and its applications, 1977, 2,no. 3, p.94-95(in Russian)