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Journal of Spectral Theory


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Volume 6, Issue 1, 2016, pp. 89–97
DOI: 10.4171/JST/119

Published online: 2016-04-04

On the spectra of the Sturm–Liouville operator with the fast oscillating potential

Rais S. Ismagilov[1]

(1) Bauman Moscow State Technical University, Russian Federation

A spectral Problem for a Sturm–Liouville operator is considered in the functional Hilbert space on the half axis. The potential is "fast oscillating". The conditions giving a discrete spectra are indicated. The spectral asymptotic is determined.

Keywords: Sturm–Liouville operator, discrete spectra, oscillating potential

Ismagilov Rais: On the spectra of the Sturm–Liouville operator with the fast oscillating potential. J. Spectr. Theory 6 (2016), 89-97. doi: 10.4171/JST/119