Open AccessOn Lacunas in the Lower Part of the Spectrum of the Periodic Magnetic Operator in a Strip
Author(s) -
Д. И. Борисов
Publication year - 2017
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2017-63-3-373-391
Subject(s) - spectrum (functional analysis) , operator (biology) , essential spectrum , mathematics , discrete spectrum , mathematical analysis , period (music) , mathematical physics , physics , geometry , quantum mechanics , chemistry , eigenvalues and eigenvectors , acoustics , biochemistry , repressor , transcription factor , gene
We consider the Schro¨dinger periodic magnetic operator in an innite at straight strip. We prove that if the magnetic potential satises 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.