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Title: On Necessary Conditions Of Basicity Of A System Of Eigen-Functions Of Second Order Discontinuous Operators
Authors: Kerimov, Nazim B.
Ibadov, Elchin J.
Issue Date: 2006
Citation: Transactions of National Academy of Sciences of Azerbaijan
Series/Report no.: Vol. 26;
Abstract: In the paper the basicity properties of a system of eigen-functions of the differential operator Lu = u 00+q (x) u are investigated, where q (x) is a complexvalued potential from the space L1 (0, 1). Following V.A.Ilin we proceed from the generalized treatment of eigen-functions and they can have discontinuity of the first order. The necessary conditions of basicity of a system of eigen-functions in the space Lp (1 < p < ∞) in terms of eigen-values are obtained.
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