 01337 Yu. Karpeshina
 On Spectral Properties of Periodic Polyharmonic Matrix Operators.
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Sep 24, 01

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Abstract. We consider a matrix operator $H=(\Delta )^l+ V
$ in $R^n$, where $n\geq 2$, $l\geq 1$, $4l>n+1$, and $V$ is the
operator of multiplication by a periodic in $x$ matrix $V(x)$. We
study spectral properties of $H$ in the high energy region.
Asymptotic formulae for Bloch eigenvalues and the corresponding
spectral projections are constructed. The BetheSommerfeld
conjecture, stating that the spectrum of $H$ can have only a
finite number of gaps, is proved.
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