Asymptotic behavior on (-a, 0) of the spectral measures of a family of singular Sturm-Liouville operatorsстатья
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Аннотация:We find the asymptotics as lambda/E > -> -a of the density of the spectral measure of the Sturm-Liouville operator in L (2)(0,+a) generated by the expression -yaEuro(3) + E > q(x)y, E > > 0, with the boundary condition y(0) cos alpha+y'(0) sin alpha = 0. The potential q(x) tends to -a as x -> +a and is assumed to satisfy the Sears condition and some additional regularity conditions.