Abstract
In this article we obtain the asymptotic formulas for eigenfunctions and eigenvalues of the nonself-adjoint Sturm-Liouville operators with periodic and antiperiodic boundary conditions, when the potential is an arbitrary summable complex-valued function. Then using these asymptotic formulas, we find the conditions on Fourier coefficients of the potential for which the eigenfunctions and associated functions of these operators form a Riesz basis inL 2(0, 1).
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Dernek, N., Veliev, O.A. On the riesz basisness of the root functions of the nonself-adjoint sturm-liouville operator. Isr. J. Math. 145, 113–123 (2005). https://doi.org/10.1007/BF02786687
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DOI: https://doi.org/10.1007/BF02786687