Abstract
We consider the spaces of sequences that arise in the inverse spectral problem for a harmonic oscillator perturbed by potential. We establish embedding theorems which connect such spaces with weight spaces \(\ell _r^2 \). We also study the approximation of elements by finite sequences.This problem arises if we restore the potential from its spectrum.Bibliography: 5 titles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. Chelkak, P. Kargaev, and E. Korotyaev, Inverse problem for harmonic oscillator perturbed by potential, characterization, Preprint SFB 288, No 73, Berlin, 2002
A. Zigmund, Trigonometric Series, Vol. 1, Cambridge, (1988)
H. P. McKean and E. Trubowitz, “The spectral class of the quantum-mechanical harmonic oscillator,” Commun. Math. Phys., 82, No. 4, 471–495(1981/82)
P. P¨ oschel and E. Trubowitz, Inverse Spectral Theory,Academic Press, Boston (1987)
G. H. Hardy, D. E. Littlewood, and G. P´ olya, Inequalities, Cambridge University Press, Cambridge (1988)
Rights and permissions
About this article
Cite this article
Chelkak, D. Approximation in the Space of Spectral Data of a Perturbed Harmonic Oscillator. Journal of Mathematical Sciences 117, 4260–4269 (2003). https://doi.org/10.1023/A:1024824821966
Issue Date:
DOI: https://doi.org/10.1023/A:1024824821966