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On Hill's operator with a matrix potential
Author(s) -
Veliev O. A.
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510682
Subject(s) - mathematics , eigenfunction , quasiperiodic function , eigenvalues and eigenvectors , operator (biology) , spectrum (functional analysis) , boundary value problem , matrix (chemical analysis) , mathematical analysis , boundary (topology) , mathematical physics , quantum mechanics , physics , biochemistry , chemistry , materials science , repressor , transcription factor , composite material , gene
In this article we obtain asymptotic formulas for eigenvalues and eigenfunctions of the self‐adjoint operator generated by a system of Sturm–Liouville equations with summable coefficients and quasiperiodic boundary conditions. Then using these asymptotic formulas, we find conditions on the potential for which the number of gaps in the spectrum of the Hill's operator with matrix potential is finite. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)