First‐order systems in
on
with periodic matrix potentials and vanishing instability intervals |
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Authors: | Sonja Currie Thomas T Roth Bruce A Watson |
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Institution: | School of Mathematics, University of the Witwatersrand, Private Bag 3, P O WITS 2050, South Africa |
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Abstract: | First‐order systems in on 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. |
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Keywords: | canonical systems inverse problems periodic eigenvalue problem Hill's equation |
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