Abstract
The differential operatorly=y″+q(x)y with periodic (antiperiodic) boundary conditions that are not strongly regular is studied. It is assumed thatq(x) is a complex-valued function of classC (4)[0, 1] andq(0)≠q(1). We prove that the system of root functions of this operator forms a Riesz basis in the spaceL 2(0, 1).
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References
V. P. Mikhailov, “On Riesz bases inL 2(0, 1),”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],144, No. 5, 981–984 (1962).
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)], No. 2, 82–93 (1964).
N. Dunford and J. T. Schwartz,Linear Operators. Pt. 3. Spectral Operators, Wiley, New York, (1971).
A. A. Shkalikov, “On the basis property of eigenfunctions of an ordinary differential operator,”Uspekhi Mat. Nauk [Russian Math. Surveys],34, No. 5, 235–236 (1979).
A. A. Shkalikov, “On the basis property of eigenfunctions of an ordinary differential operator with integral boundary conditions,”Vestnik Moskov. Univ. Ser. I Mat. Mekh. [Moscow Univ. Math. Bull.], No. 6, 12–21 (1982).
M. A. Naimark,Linear Differential Operators [in Russian], Nauka, Moscow (1969).
S. Kaczmarz and H. Steinhaus,Theorie der Orthogonalreihen, Warsaw-Lvov (1935); Russian translation: Inostr. Lit., Moscow (1958).
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Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 558–563, October, 1998.
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Kerimov, N.B., Mamedov, K.R. On the Riesz basis property of the root functions in certain regular boundary value problems. Math Notes 64, 483–487 (1998). https://doi.org/10.1007/BF02314629
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DOI: https://doi.org/10.1007/BF02314629