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On Eigenvalues of Nonlinear Operator Pencils with Many Parameters
Current Issue
Volume 3, 2015
Issue 4 (August)
Pages: 96-100   |   Vol. 3, No. 4, August 2015   |   Follow on         
Paper in PDF Downloads: 32   Since Aug. 28, 2015 Views: 1667   Since Aug. 28, 2015
Authors
[1]
Rakhshanda Dzhabarzadeh, Department of Functional Analysis, Institite of Mathematics Ana Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.
[2]
Gunay Salmanova, Department of Algebra and Geometry, Ganja State Universitety, Ganja, Azerbaijan.
Abstract
The authors give the necessary and sufficient conditions of the existence of the common eigenvalues of the nonlinear several operator pencils with many parameters. The operator pencils contain also the products of these parameters in finite degree. The number of equations in these systems may be more, than the number of parameters. In the proof the authors essentially use the results of multiparameter spectral theory and the notion of the analog resultant of two and several operator pencils in many parameters.
Keywords
Resultant, Operator, Multiparameter System, Eigenvalue
Reference
[1]
Atkinson F. V. Multiparameter spectral theory. Bull.Amer.Math.Soc.1968, 74, 1-27.
[2]
Browne P.J. Multiparameter spectral theory. Indiana Univ. Math. J, 24, 3, 1974.
[3]
Sleeman B. D. Multiparameter spectral theory in Hilbert space. Pitnam Press, London, 1978, p.118.
[4]
Dzhabarzadeh R.M. Spectral theory of multiparameter system of operators in Hilbert space, Transactions of NAS of Azerbaijan, 1-2, 1999, 33-40.
[5]
Dzhabarzadeh R. M, Salmanova G. H. Multtiparameter system of operators, not linearly depending on parameters. American Journal of Mathematics and Mathematical Sciences. 2012, vol.1, No.2.- p.39-45.
[6]
Dzhabarzadeh R.M. Spectral theory of two parameter s system in finite-dimensional space. Transactions of NAS of Azerbaijan, v. 3-4 1998, p.12-18.
[7]
Balinskii A.I (Балинский) Generation of notions of Обобщение понятия Bezutiant and Resultant DAN of Ukr. SSR, ser.ph.-math and tech. of sciences, 1980,2. (in Russian).
[8]
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[9]
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.
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