Spectral properties of complex Airy operator on the semi-axisстатья
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Аннотация:We prove a theorem on the completeness of the system of root functions of the Schrödinger operator L = −d2/dx2 + p(x) on the half-line R+ with a potential p for which L appears to be maximal sectorial. An application of this theorem to the complex Airy operator Lc = −d2/dx2 + cx, c = const, implies the completeness of the system of eigenfunctions of Lc for the case in which |arg c| < 2π/3.We use subtler methods to prove a theorem stating that the system of eigenfunctions of this special operator remains complete under the condition that |arg c| < 5π/6.