Spectral gaps of the one-dimensional Schrödinger operators with singular periodic potentials
| dc.creator | Mikhailets, Vladimir | |
| dc.creator | Molyboga, Volodymyr | |
| dc.date | 2008-05-14 | |
| dc.date | 2009-04-06 | |
| dc.date.accessioned | 2026-07-07T12:59:57Z | |
| dc.date.available | 2026-07-07T12:59:57Z | |
| dc.description | The behaviour of the lengths of spectral gaps $\{γ_{n}(q)\}_{n=1}^{\infty}$ of the Hill-Schrödinger operators S(q)u=-u''+q(x)u,\quad u\in \mathrm{Dom}(S(q)) with real-valued 1-periodic distributional potentials $q(x)\in H_{1{-}per}^{-1}(\mathbb{R})$ is studied. We show that they exhibit the same behaviour as the Fourier coefficients $\{\widehat{q}(n)\}_{n=-\infty}^{\infty}$ of the potentials $q(x)$ with respect to the weighted sequence spaces $h^{s,φ}$, $s>-1$, $φ\in \mathrm{SV}$. The case $q(x)\in L_{1{-}per}^{2}(\mathbb{R})$, $s\in \mathbb{Z}_{+}$, $φ\equiv 1$ corresponds to the Marchenko-Ostrovskii Theorem. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/0805.2136 | |
| dc.identifier | http://arxiv.org/abs/0805.2136 | |
| dc.identifier | Methods Funct. Anal. Topology 15 (2009), no. 1, 31-40 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225733 | |
| dc.subject | Spectral Theory | |
| dc.subject | 34L40 (Primary), 47A10, 47A75 (Secondary) | |
| dc.title | Spectral gaps of the one-dimensional Schrödinger operators with singular periodic potentials | |
| dc.type | text |