On spectral properties of periodic polyharmonic matrix operators
We consider a matrix operatorH = (-Δ)l +V inRn, wheren ≥ 2,l ≥ 1, 4l > n + 1, andV is the operator of multiplication by a periodic inx matrixV(x). We study spectral properties ofH in the high energy region. Asymptotic formulae for Bloch eigenvalues and the corresponding spectral projections are constructed. The Bethe-Sommerfeld conjecture, stating that the spectrum ofH can have only a finite number of gaps, is proved.
Volume 131, 2021
Continuous Article Publishing mode
Click here for Editorial Note on CAP Mode