Geodesic
On spectral perturbation caused by bounded variation of potential
Sbornik. Mathematics, Tome 205 (2014) no. 1, pp. 1-6 Cet article a éte moissonné depuis la source Math-Net.Ru

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The harmonic oscillator operator is perturbed by an arbitrary bounded continuous term. This results in the perturbation of the spectrum. The map sending the first of these perturbations into the second is examined. Its approximation by a linear map is studied. Bibliography: 2 titles.
Keywords: harmonic oscillator, spectrum, Sturm-Liouville operator.
Mots-clés : perturbation 
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R. S. Ismagilov. On spectral perturbation caused by bounded variation of potential. Sbornik. Mathematics, Tome 205 (2014) no. 1, pp. 1-6. http://geodesic.mathdoc.fr/item/SM_2014_205_1_a0/

[1] R. S. Ismagilov, A. G. Kostyuchenko, “Perturbation of the spectrum of a differential operator under a bounded perturbation of the potential”, Funct. Anal. Appl., 43:3 (2009), 208–216 | DOI | DOI | MR | Zbl

[2] N. N. Lebedev, Special functions and their applications, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965, xii+308 pp. | MR | MR | Zbl | Zbl