Geodesic
Some singular perturbations of periodic operators
Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 2, pp. 207-218

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We consider two examples of singular perturbations of a periodic differential operator on the axis. The first example is a rapidly oscillating potential with compact support, and the second example is the delta potential with a small complex coupling constant. We investigate the structure and asymptotic behavior of the spectrum of the perturbed operators in detail.
Mots-clés : perturbation
Keywords: periodic operator, spectrum, asymptotic expansion. 
@article{TMF_2007_151_2_a2,
     author = {D. I. Borisov},
     title = {Some singular perturbations of periodic operators},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {207--218},
     publisher = {mathdoc},
     volume = {151},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_151_2_a2/}
}
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D. I. Borisov. Some singular perturbations of periodic operators. Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 2, pp. 207-218. http://geodesic.mathdoc.fr/item/TMF_2007_151_2_a2/