Pure and Applied Mathematics Journal
Volume 4, Issue 4-1, August 2015, Pages: 22-26
Received: Apr. 29, 2015;
Accepted: May 14, 2015;
Published: Aug. 21, 2015
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Rakhshanda Dzhabarzadeh, Department of functional analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan
The theorem on possibility of multiple summation of the series on eigen and associated vectors of the operator pencil in the Hilbert space is proved. Research of multiple completeness and multiple expansions of eigen and associated vectors of such operator pencils are closely connected with the research of differential operator equation with the boundary conditions
Spectral Theory of Operator Pencils in the Hilbert Spaces, Pure and Applied Mathematics Journal. Special Issue: Spectral Theory of Multiparameter Operator Pencils and Its Applications.
Vol. 4, No. 4-1,
2015, pp. 22-26.
Keldysh M.V. About completeness of eigen functions of some class linear non-selfadjoint operators. Journal Success of Mathematical Science .1971, т.27, issue.4,p.15-47
Dzhabarzadeh R.M. On expansions series on eigen and associated vectors of operator pencils Journal: Scientific notes of Azerb.State University,1964, №3,pp.75-81.
Vizitei V.N., Markus A.S. On convergence of multiple expansions on the system of eigen and associated vectors of polynomial pencils /Mathematical collection,1965,т.66, №2, pp..287-320
Gokhberg I.Ts., Kreyn M.Q. Introduction to the theory of linear non-selfadjoint operators in the Hilbert space.Moscow,1964, pp 1-433.
Allakhverdiev J.E., Dzhabarzadeh R. M. // Spectral theory of operator pencil in the Hilbert space. ДAN of Azerbaijan, 2011, т.LXVII, № 4., pр.3-10.
Allakhverdiev J.E.,Dzhabarzadeh R.M. Оn summation of multiple series on eigen and associated vectors of operator pencils by Abel’s method. ДАN Аz SSR, 1979,т.35, № 7,p 19-23.
Lidskii V.B.. About summation of the series on the general vectors of the non-selfadjoint operators. Proceeding of Moscow Scientific Society, t.11, 1962.
Radzievskii Q.V.Multiple completeness of root vectors of Keldysh’s operator pencil, disturbing by analytical operatorfunction.DAN USSR,ser.A,1976,,7,pp.597-600.
Dzhabarzadeh R. M. To the spectral theory of polynomial pencils.Proceedinfg of Oryol State Universitety Russia ,2006,t.1,pp.161-165.