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Asymptotics of instability zones of the Hill operator with a two term potential |
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| Authors: | Plamen Djakov Boris Mityagin |
| Affiliation: | a Department of Mathematics, Sofia University, 1164 Sofia, Bulgaria b Department of Mathematics, The Ohio State University, 231 West 18th Ave, Columbus, OH 43210, USA |
| Abstract: | Let γn denote the length of the nth zone of instability of the Hill operator Ly=−y″−[4tαcos2x+2α2cos4x]y, where α≠0, and either both α, t are real, or both are pure imaginary numbers. For even n we prove: if t, n are fixed, then for α→0  |
| Keywords: | Hill operator Two-term potential Asymptotics of spectral gaps |
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