Singularly perturbed periodic and semiperiodic differential operators

Details Singularly perturbed periodic and semiperiodic differential operators Singularly perturbed periodic and semiperiodic differential operators

2007-05-21

arxiv.org/abs/0705.3045v1

Ukrainian Math. J. 59 (2007), no. 6, 785-797

Mathematics

Functional Analysis

13 pages

Scientific paper

10.1007/s11253-007-0055-7

Qualitative and spectral properties of the form-sums S_{\pm}(V):=D_{\pm}^{2m}\dotplus V(x),\quad m\in \mathbb{N}, in the Hilbert space $L_{2}(0,1)$ are studied. Here the periodic $(D_{+})$ and the semiperiodic $(D_{-})$ differential operators are $D_{\pm}: u\mapsto -i u'$, and $V(x)$ is a 1-periodic complex-valued distribution in the Sobolev spaces $H_{per}^{-m\alpha}$, $\alpha\in [0,1]$.

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