We study the Rellich type theorem (RT) for the Maxwell operator $\hat H^D=\hat D\hat H_0$ on ${ \bf Z}^3$ with constant anisotropic medium, i.e. the permittivity and permeability of which are non-scalar constant diagonal matrices. We also study the unique continuation theorem for the perturbed Maxwell operator $\hat H^{ D_p}=\hat { D}_p\hat H_0$ on ${ \bf Z}^3$ where the permittivity and permeability are locally perturbed from a constant matrix on a compact set in ${ \bf Z}^3$. It then implies that, if $\hat H^D- \lambda$ satisfies (RT), then all distributions $\hat u$ in Besov space $\mathcal B_0^{ \ast}({ \bf Z}^3;{ \bf C}^3)$ satisfying the equation $(\hat H^{ D_p} - \lambda) \hat u = 0$ outside a compact set vanish near infinity.
Categories: math.AP