Spectral Problems of Multiparameter System of Operators with Two Parameters
[1]
Rakhshanda Dzhabarzadeh, Department of Functional Analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.
[2]
Afet Jabrailova, Department of Functional Analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.
In this paper sufficient conditions of the existence of multiple completeness of the eigen and associated vectors of two parameter system of operators in the Hilbert space are given. In the special case when the spaces have the finite dimensions these sufficient conditions are also necessary. The operators in the multiparameter system are not necessarily selfadjoint. The method, used in the work, allows to consider a system with a complex dependence on the parameters.The proof uses the notion of the abstract analog of resultant of two operator pencils, acting, generally speaking, in different Hilbert spaces.
Multiparameter, Spectrum, Operator, Space, Eigenvector
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