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On the riesz basisness of the root functions of the nonself-adjoint sturm-liouville operator

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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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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Science, Marmara University Göztepe Kampüsü, 81040, Kadiköy, Istanbul, Turkey

    Neşe Dernek

  2. Departartment of Mathematics, Faculty of Arts and Science, Dogus University Acibadem, 34722, Kadiköy, Istanbul, Turkey

    O. A. Veliev

Authors
  1. Neşe Dernek
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  2. O. A. Veliev
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Correspondence to Neşe Dernek.

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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

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