On the eigenvalues of a polyharmonic matrix operator near diffraction planes
Sedef Karakılıç, Setenay Akduman · AIP conference proceedings · 2021
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=(x1,x2,⋯,xd)∈ℝd, d≥2,12<l<1. We obtain the high energy asymptotics for the eigenvalues of this operator which lies near the diffraction planes.