A RELLICH TYPE THEOREM FOR DISCRETE MAXWELL OPERATORS
Résumé
Abstract. We study the Rellich type theorem (RT) for the Maxwell operator
Ĥ D = D̂Ĥ0 on Z3 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
Ĥ Dp = D̂p Ĥ0 on Z3 where the permittivity and permeability are locally
perturbed from a constant matrix on a compact set in Z3 . It then implies that,
if Ĥ D − λ satisfies (RT), then all distributions û in Besov space B0∗ (Z3 ; C3 )
satisfying the equation (Ĥ Dp − λ)û = 0 outside a compact set vanish near
infinity.
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