Persistence of point spectrum for perturbations of one-dimensional operators with discrete spectra. (English) Zbl 1521.47057
Miranda, Pablo (ed.) et al., Spectral theory and mathematical physics. Proceedings of the conference, STMP 2018, Santiago, Chile, December 3–7, 2018. Cham: Springer. Lat. Am. Math. Ser., 125-151 (2020).
Summary: Sufficient conditions are given, for the preservation of the pure point spectrum, as well as dynamical localization properties, of autonomous and time-periodic perturbations of self-adjoint operators in \(\ell^2(\mathbb{Z})\) with simple pure point spectra whose eigenvalues have no accumulation point.
For the entire collection see [Zbl 1461.35006].
For the entire collection see [Zbl 1461.35006].
MSC:
| 47B39 | Linear difference operators |
| 81Q15 | Perturbation theories for operators and differential equations in quantum theory |
| 47A10 | Spectrum, resolvent |
