, Volume 129, Issue 4, pp 4053-4082

Asymptotics of Spectral Data of a Harmonic Oscillator Perturbed by a Potential

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Abstract

Asymptotics of spectral data of a perturbed harmonic oscillator −y″ + x2y + q(x)y are obtained for potentials q(x) such that q′, xq ∈ L2(ℝ). These results are important in the solution of the corresponding inverse spectral problem. Bibliography: 7 titles.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 303, 2003, pp. 223–271.