Bessel Property of the System of Root Functions of a Second-Order Singular Operator on an Interval |
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Authors: | L V Kritskov |
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Institution: | 1.Lomonosov Moscow State University,Moscow,Russia |
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Abstract: | For the system of root functions of an operator defined by the differential operation ?u″ + p(x)u′ + q(x)u, x ∈ G = (0, 1), with complex-valued singular coefficients, sufficient conditions for the Bessel property in the space L2(G) are obtained and a theorem on the unconditional basis property is proved. It is assumed that the functions p(x) and q(x) locally belong to the spaces L2 and W2?1, respectively, and may have singularities at the endpoints of G such that q(x) = qR(x) +q′S(x) and the functions qS(x), p(x), q 2 S (x)w(x), p2(x)w(x), and qR(x)w(x) are integrable on the whole interval G, where w(x) = x(1 ? x). |
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