Geodesic
On lacunas in the lower part of the spectrum of the periodic magnetic operator in a~strip
Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 63 (2017) no. 3, pp. 373-391

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We consider the Schrödinger periodic magnetic operator in an infinite flat straight strip. We prove that if the magnetic potential satisfies certain conditions and the period is small enough, then the lower part of the band spectrum has no inner lacunas. The length of the lower part of the band spectrum with no inner lacunas is calculated explicitly. The upper estimate for the small parameter allowing these results is calculated as a number as well. 
@article{CMFD_2017_63_3_a0,
     author = {D. I. Borisov},
     title = {On lacunas in the lower part of the spectrum of the periodic magnetic operator in a~strip},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {373--391},
     publisher = {mathdoc},
     volume = {63},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2017_63_3_a0/}
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D. I. Borisov. On lacunas in the lower part of the spectrum of the periodic magnetic operator in a~strip. Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 63 (2017) no. 3, pp. 373-391. http://geodesic.mathdoc.fr/item/CMFD_2017_63_3_a0/