Volume 4, Issue 4-1, August 2015, Page: 5-10
Multiparameter Operator Systems with Three Parameters
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
Received: Feb. 25, 2015;       Accepted: Feb. 27, 2015;       Published: May 12, 2015
DOI: 10.11648/j.pamj.s.2015040401.12      View  3726      Downloads  72
Abstract
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.
Keywords
Eigen and Associated Vectors, Finite Dimensional Space, Multiparameter System of Operators, Nonlinear Algebraic System of Equations, Resultant-Operator of Two Pencils
To cite this article
Rakhshanda Dzhabarzadeh, Kamilla Alimardanova, 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. doi: 10.11648/j.pamj.s.2015040401.12
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