Annales Henri Poincaré

, Volume 9, Issue 3, pp 457–508 | Cite as

Bethe–Sommerfeld Conjecture

  • Leonid ParnovskiEmail author


We consider Schrödinger operator −Δ + V in \({\mathbb{R}}^d (d \geq 2)\) with smooth periodic potential V and prove that there are only finitely many gaps in its spectrum.


Asymptotic Formula Conjugate Point Integer Vector Operator Pencil Compact Resolvent 
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Copyright information

© Birkhaueser 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity College LondonLondonUnited Kingdom

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