Asymptotics of instability zones of Hill operators with a two term potential

Plamen Djakov; Boris Mityagin

doi:10.1016/j.crma.2004.06.019

Partial Differential Equations/Ordinary Differential Equations

Asymptotics of instability zones of Hill operators with a two term potential

Presented by: Alain Connes

Plamen Djakov ¹; Boris Mityagin ²

¹ Department of Mathematics, Sofia University, 1164 Sofia, Bulgaria
² Department of Mathematics, The Ohio State University, 231, West 18th Ave, Columbus, OH 43210, USA

Comptes Rendus. Mathématique, Volume 339 (2004) no. 5, pp. 351-354.

Abstract
Résumé

We give a sharp asymptotics of the instability zones of the Hill operator $L y = - y^{″} + (a cos 2 x + b cos 4 x) y$ for arbitrary real $a, b \neq 0$ .

Dans cette Note on donne une estimation asymptotique des intervalles d'instabilité d'opérateurs de Hill de la forme $L y = - y^{″} + (a cos 2 x + b cos 4 x) y,$ où a et b sont des réels non nuls arbitraires.

Received: 2004-03-30
Accepted: 2004-06-22
Published online: 2004-08-10

DOI: 10.1016/j.crma.2004.06.019

Author's affiliations:

Plamen Djakov ¹; Boris Mityagin ²

¹ Department of Mathematics, Sofia University, 1164 Sofia, Bulgaria
² Department of Mathematics, The Ohio State University, 231, West 18th Ave, Columbus, OH 43210, USA

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     title = {Asymptotics of instability zones of {Hill} operators with a two term potential},
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     year = {2004},
     doi = {10.1016/j.crma.2004.06.019},
     language = {en},
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Plamen Djakov; Boris Mityagin. Asymptotics of instability zones of Hill operators with a two term potential. Comptes Rendus. Mathématique, Volume 339 (2004) no. 5, pp. 351-354. doi : 10.1016/j.crma.2004.06.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.06.019/

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