A note on discrete Borg-type theorems |
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Authors: | V B Kiran Kumar G Krishna Kumar |
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Institution: | 1. Department of Mathematics, Cochin University of Science and Technology, Kochi, India.;2. Department of Mathematics, BJM Government College, Chavara, Chavara, India. |
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Abstract: | We consider the discrete versions of the well-known Borg’s theorem and use simple linear algebraic techniques to obtain new versions of the discrete Borg-type theorems. To be precise, we prove that the periodic potential of a discrete Schrödinger operator is almost a constant if and only if the possible spectral gaps of the operator are of small width. This result is further extended to more general settings and the connection to the well-known Ten Martini problem is also discussed. |
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Keywords: | Spectrum Schrödinger operator Laurent–Toeplitz operator Borg-type theorems |
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