On the Basis Property in Lp( 0,1) of the Root Functions of Non-self Adjoint Sturm-Lioville Operators

[1] N K Bari. Biorthogonal systems and bases in Hilbert spaces. Uchen. Zap. Moskov. Gos.
Univ. 148(4):68-107, 1951 (Russian).
[2] N Dernek and O A Veliev. On the Riesz basisness of the root functions of the nonselfadjoint
Sturm-Liouville operators. Israel Journal of Mathematics, 145:113-123, 2005.
[3] P Djakov and B S Mitjagin. Instability Zones of Periodic 1-dimensional Schrodinger and
Dirac Operators. Uspekhi Mat. Nauk, 61:4, 77-182, 2006. English Transl. in Russian
Math. Surves, 61:4, 663-776, 2006.
[4] N Dunford and J T Schwartz. Linear Operators, Prt.3 Spectral Operators. Wiley, New
York, 1970.
[5] I C Gohberg and M G Krein. Introduction to the Theory of Linear Nonselfadjoint Operators.
American Math. Soc., Providence, Rhode Island, 1969.
[6] N I Ionkin. The solution of a boundary-value problem in heat conduction with a nonclassical
boundary condition. Differ. Equations, 13(2): 294-304, 1977.
[7] B S Kashin and A A Saakyan. Orthogonal Series. American Mathematical Society, 1989.
[8] N B Kerimov and Kh R Mamedov. On the Riesz basis property of the root functions in
certain regular boundary value problems. Math. Notes, 64(4): 483-487, 1998.
[9] G M Kesel’man. On the unconditional convergence of expansions in the eigenfunctions
of some differential operators, Izv. Vyssh. Uchebn. Zaved. Mat. [Soviet Math. (Iz. VUZ)],
2: 82-93, 1964.
[10] A A Kıraç. Riesz Basis Property of the Root functions of non-selfadjoint operators wit
regular boundary conditions, Int.Journal of Math.Analysis. 3(22):1101-1109, 2009.
[11] V M Kurbanov. A theorem on equivalent bases for a differential operator. Dokl. Akad.
Nauk, 406(1):17-20, 2006.
[12] A S Makin. Convergence of expansions in the root functions of periodic boundary value
problems. Doklady Math., 73(1):71-76, 2006.
[13] A S Makin. On spectral decompositions corresponding to non-self-adjoint Sturm-Lioville
operators. Doklady Math., 73(1):15-18, 2006.
[14] Kh R Mamedov. On spectrally of differential operator of second order. Proceeding of
Institute of Mathematics and Mechanics, Acad, Sci. Azer. Repub. 5:179-181, 1996.
[15] Kh R Mamedov and H Menken. On the basisness in L2(0,1) of the root functions in
not strongly regular boundary value problems. European Journal of Pure and Applied
Math.,1(2):51-60, 2008.
[16] H Menken and Kh R Mamedov. Basis property in Lp(0,1) of the root functıons correspondıng
to a boundary-value problem. Journal of Applied Functional Analysis, 5(4):351-
356, 2010.
[17] V P Mikhailov. On the bases in L2(0,1). Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],
144(5): 981-984, 1962.
[18] M A Naimark. Linear Differential Operators, Part I. Frederick Ungar Pub. Co., New York,
1967.
[19] A A Shkalikov. On the Riesz basis property of the root vectors of ordinary differential
operators. Russian Math. Surveys, 34(5):249-250, 1979.
[20] A A Shkalikov. On the basis property of the eigenfunctions of ordinary differential operators
with integral boundary conditions. Vestnik Moscow University, Ser. Mat. Mekh.,
37(6):12-21, 1982.
[21] O A Veliev and A A Shkalikov. On the Riesz Basis Property of the Eigen- and Associated
Functions of Periodic and Antiperiodic Sturm–Liouville Problems. Mat. Zametki,
85(5):671–686, 2009.
[22] A Zygmund. Trigonometric Series, Vol. 2. Cambridge Univ. Press, Cambridge, 1959.