arXiv
Open Access
2019
Bethe-Sommerfeld conjecture in semiclassical settings
Victor Ivrii
Abstrak
Under certain assumptions (including $d\ge 2)$ we prove that the spectrum of a scalar operator in $\mathscr{L}^2(\mathbb{R}^d)$ \begin{equation*} A_\varepsilon (x,hD)= A^0(hD) + \varepsilon B(x,hD), \end{equation*} covers interval $(τ-ε,τ+ε)$, where $A^0$ is an elliptic operator and $B(x,hD)$ is a periodic perturbation, $\varepsilon=O(h^\varkappa)$, $\varkappa>0$. Further, we consider generalizations.
Topik & Kata Kunci
Penulis (1)
V
Victor Ivrii
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2019
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓