Sharp asymptotics of the quasimomentum
classification
🧮 math.SP
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asymptoticsfunctionsquasimomentumassumebelongsblochcircleconsider
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We consider the Schr\"odinger operator with a periodic potential $p$ on the real line. We assume that $p$ belongs to the Sobolev space $\mH_m$ on the circle for some $m\ge -1$, and we determine the asymptotics of the quasimomentum and the Titchmarsh-Weyl functions, the Bloch functions at high energy.
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