D. I. Borisov, “On lacunas in the lower part of the spectrum of the periodic magnetic operator in a strip”, CMFD, 2017, Volume 63, Issue 3,Pages <nobr>373

This article is cited in 3 papers

On lacunas in the lower part of the spectrum of the periodic magnetic operator in a strip

D. I. Borisov^abc

^a Institute of Mathematics with Computer Center, Ufa Science Center, Russian Academy of Sciences, 112 Chernyshevskogo st., 450008 Ufa, Russia
^b Bashkir State Pedagogical University, 3a Oktyabr'skoy Revolutsii st., 450000 Ufa, Russia
^c University of Hradec Králové, 62 Rokitanského st., 500 03 Hradec Králové, Czech Republic

Abstract: 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.

UDC: 517.958+517.984+519.21

DOI: 10.22363/2413-3639-2017-63-3-373-391