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Relation between smoothness of the potential and size of gaps in the essential spectrum of a Schrödinger operator

✍ Scribed by E. D. Belokolos; I. M. Pershko


Book ID
112478304
Publisher
Springer
Year
1982
Tongue
English
Weight
357 KB
Volume
33
Category
Article
ISSN
0041-5995

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Smoothness of Schrödinger Operator Poten
✍ Plamen Djakov; Boris Mityagin 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 281 KB

Consider the Schro¨dinger equation Ày 00 þ V ðxÞy ¼ ly with a periodic real-valued L 2 -potential V of period 1; VðxÞ ¼ P 1 m¼À1 vðmÞ expð2pimxÞ: Let fl À n ; l þ n g be its zones of instability, i.e. fl À n ; l þ n g are pairs of periodic and antiperiodic eigenvalues, and b 2 ð0; 1Þ determines Gevr