First‐order systems in C2 on R with periodic matrix potentials and vanishing instability intervals. (19th December 2014)

• Record Type: Journal Article
• Authors: Currie, Sonja; Roth, Thomas T.; Watson, Bruce A.
• Is Part Of: Mathematical methods in the applied sciences. Volume 38:Number 17(2015:Nov. 30)
• Page Start: 4435
• Page End: 4447
• Publication Date: 2014-12-19
• Subjects: canonical systems -- inverse problems -- periodic eigenvalue problem -- Hill's equation; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3382
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : First‐order systems in C 2 on R with absolutely continuous real symmetric π ‐periodic matrix potentials are considered. A thorough analysis of the discriminant is given. Interlacing of the eigenvalues of the periodic, antiperiodic and Dirichlet‐type boundary value problems on [0, π ] is shown for a suitable indexing of the eigenvalues. The periodic and antiperiodic eigenvalues are characterized in terms of Dirichlet‐type eigenvalues. It is shown that all instability intervals vanish if and only if the potential is the product of an absolutely continuous real scalar valued function with the identity matrix. Copyright © 2014 John Wiley & Sons, Ltd.