Pure and Applied Mathematics Journal
Volume 2, Issue 1, February 2013, Pages: 32-37
Received: Jan. 25, 2013;
Published: Feb. 20, 2013
Views 3292 Downloads 138
Rakhshanda Dzhabarzadeh, İnstitute Mathematics and Mechanics of NAN of Azerbaijan, Baku
For nonlinear algebraic system with two variables sufficient conditions of existence of solutions are given. The proof of these statements is received as a corollary of more common reviewing considered in this paper. In particular, in this work the existence of multiple base on eigen and associated vectors of a two parameter system of operators in fi-nite-dimensional spaces is proved. Definitions of the associated vectors, multiple completeness of eigen and associated vectors of two-parameter not selfadjoint systems, nonlinearly depending on spectral parameters are introduced. At the proof of these results we essentially used the notion of the analog of an resultant of two polynomial bundles.
About Solutions of Nonlinear Algebraic System with Two Variables, Pure and Applied Mathematics Journal.
Vol. 2, No. 1,
2013, pp. 32-37.
Atkinson F.V. Multiparameter spectral theory. Bull.Amer.Math.Soc.1968, 74, 1-27
Balinskii A.I Generation of notions of Bezutiant and Re-sultant DAN of Ukr SSR, ser.ph.-math and tech. of sciences,1980, 2, pp.3-6( in Russian).
Browne P.J. Multiparameter spectral theory. Indiana Univ. Math. J,24, 3, 1974.
Dzhabarzadeh R.M. On existence of common eigen value of some operator-bundles, that depends polynomial on parameter. International conference of topology, 3-9 oct., 1987, Baku. Tez., part 2,page 99
Dzhabarzadeh R.M. Spectral theory of two parameter system in finite dimensional space. Transactions of Azerbaijan Na-tional Academy of Sciences, v.XVIII,3-4,pp.12-18
Dzhabarzadeh R.M. Multiparameter spectral theory. Lambert Academic Publishing , 2 mart 2012, pp.182
Prugoveĉku E. Quantum mechanics in Hilbert space. Aca-demic Press, New York, London, 1971
Sleeman B.D. Multiparameter spectral theory in Hilbert space. Pitnam Press, London, 1978, pp.118.
Hargrave B.A., Sleeman B.D. The numerical solution of two-parameter eigenvalue to the problem of diffraction by a plane angular sector. J. Inst.Math. Applic.14, 1974, 9-22.
Voytovich N.N., Katsenelenbaum B.Z., Sivov A.N.Generaliz a method of characteristic oscillations in the theory of a dif-fraction - М.: publishing "Science", 1977. - pp. 416.
Genchev Т.Q. (Генчев) About the ultraparabolic equations. DAS of USSR, 1963, т.151, №2, p.265-268 (in Russian)
Keldysh М.V. About completeness of eigenfunctions of some classes of self-conjugate linear operators. UMN, 1971, т.27, issue 4, p.15-41.(in Russian)
Levi P. (Леви). Stochastic processes and a Brownian motion. М.: publishing "Science", 1979, pp 375 (in Russian).
MarchukG.I. (Марчук) . Metody of calculation of nuclear reactors. М.: , "State Atom Publishing",1961 (in Russian).
Richmakher R (Рихмахер). Printsipy of modern mathematical physics., M. publishing "Mir", 1982,p. 486 (in Russian). Fok V.A. (Фок). The beqinnings of a quantum mechanics. М.: Publishing "Science", 1976, pp,376.
Khayniq Q (Хайниг). Abstract analog of an eliminant of two polynomial bundles. The Functional analysis and its appli-cations, 1977, 2, issue 3, pp.94-95. (in Russsian)