Resolvent Estimate of The Non-SelfadjointDi erential Operators By m-Sectorial Operators

Suppose S ⊂ Rn be bounded. Let (Ty)(x) = −Σni;j=1(t μ(x)y′xi (x))′xjbe a non - selfadjoint di erential operator on Hilbert space H = L2(S)with Dirichlet-type boundary conditions. Here, 0 ≤ ξ < 1, t ∈ [0, 1],and x ∈ S. In this paper, we investigate the spectral properties of thenon-selfadjoint di erential operator T acting on H.