Pure and Applied Mathematics Journal
Volume 4, Issue 4-1, August 2015, Pages: 11-15
Received: Mar. 23, 2015;
Accepted: Apr. 10, 2015;
Published: May 12, 2015
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Rakhshanda Dzhabarzadeh, Department of functional analysis of Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku
Elnara Sultanova, Department of Applied Mathematics of Baku State Universiteties, Azerbaijan, Baku
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.
Criterion of Existence of Eigen Values of Linear Multiparameter Systems, Pure and Applied Mathematics Journal. Special Issue: Spectral Theory of Multiparameter Operator Pencils and Its Applications.
Vol. 4, No. 4-1,
2015, pp. 11-15.
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.
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).
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, 33-40.
Dzhabarzadeh R.M. Multiparameter spectral theory. Lambert Academic Publishing, 2012, pp. 184 (in Russian).
Dzhabarzadeh R.M. Nonlinear algebraic systems. Lambert Academic Publishing, 2013, pp. 101(in Russian).
Dzhabarzadeh R. M. Common solutions of several polinomials in one or more variables. FEN-nauka, Russia ,1(40),pp.6-12 2015,Sayt 134786.
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.
Dzhabarzadeh R.M. On existence of common eigenvalues of some operator bundles polynomial depending on parameter. Baku, International Conference on Topoloji. 3-9 0ctober 1987.Tez.p-.2, Baku,p,93.
Khayniq (Хайниг Г) .Abstract analog of Resultant for two polynomial bundles Functional analyses and its applications, 1977, 2,no. 3, p.94-95.