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تسجيل مستخدم جديدBethe-Sommerfeld conjecture for pseudodifferential perturbation
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We consider a periodic pseudodifferential operator $H=(-Delta)^l+A$ ($l>0$) in $R^d$ which satisfies the following conditions: (i) the symbol of $H$ is smooth in $x$, and (ii) the perturbation $A$ has order smaller than $2l-1$. Under these assumptions, we prove that the spectrum of $H$ contains a half-line.
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