Abstract
It is shown in the Weyl limit‐point case that system of root functions of the non‐self‐adjoint Bessel operator and its perturbation Sturm–Liouville operator form a complete system in the Hilbert space. Furthermore, asymptotic behavior of the eigenvalues of the non‐self‐adjoint Bessel operators is investigated, and it is proved that system of root functions form a Bari basis in the same Hilbert space. Copyright © 2013 John Wiley & Sons, Ltd.
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