On the eigenvalues of a polyharmonic matrix operator near diffraction planes

摘要

In this study, we consider the d-dimensional polyharmonic matrix operator H(l,V)u=(-Δ)~lu+V(x)u, where (-Δ)~l is a diagonal s×s matrix, whose diagonal elements are the scalar polyharmonic operators, V is the operator of multiplication by a symmetric s×s matrix, V(x) is periodic with respect to an arbitrary lattice and s ≥ 2, x=(x_1,x_2,...,x_d)∈d, d≥2,1/2