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English

The Inverse Problem for Perturbed Harmonic Oscillator on the Half-Line with a Dirichlet Boundary Condition

Published inAnnales Henri Poincaré, vol. 8, no. 6, p. 1115-1150
Collection
  • Open Access - Licence nationale Springer 
Publication date2007
Abstract

We consider the perturbed harmonic oscillator TDψ=−ψ′′+x2ψ+q(x)ψ,ψ(0)=0, in L2(R+), where q∈H+={q′,xq∈L2(R+)} is a real-valued potential. We prove that the mapping q⟼ spectral data = {eigenvalues of T D }⊕ {norming constants} is one-to-one and onto. The complete characterization of the set of spectral data which corresponds to q∈H+ is given.

Citation (ISO format)
CHELKAK, Dmitry, KOROTYAEV, Evgeny. The Inverse Problem for Perturbed Harmonic Oscillator on the Half-Line with a Dirichlet Boundary Condition. In: Annales Henri Poincaré, 2007, vol. 8, n° 6, p. 1115–1150. doi: 10.1007/s00023-007-0330-z
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ISSN of the journal1424-0637
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