On Lacunas in the Lower Part of the Spectrum of the Periodic Magnetic Operator in a Strip

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Abstract

We consider the Schro¨dinger 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.

About the authors

Denis I Borisov

Institute of Mathematics with Computer Center, Ufa Science Center; Bashkir State Pedagogical University; University of Hradec Kra´love´

Email: borisovdi@yandex.ru
Russian Academy of Sciences, 112 Chernyshevskogo st., 450008 Ufa, Russia; 3a Oktyabr’skoy Revolutsii st., 450000 Ufa, Russia; 62 Rokitanske´ho st., 500 03 Hradec Kra´love´, Czech Republic

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