Uniform complex time heat Kernel estimates without Gaussian bounds

The aim of this article is twofold. First, we study the uniform complex time heat kernel estimates of alpha e( -z - (-Delta )alpha/2) for alpha > 0 , z is an element of C + . To this end, we establish the asymptotic estimates for P(z,x) with z satisfying 0 < omega <= divided by theta divided by < pi / 2 followed by the uniform complex time heat kernel estimates. Second, we studied the uniform complex time estimates of the analytic semigroup generated by H = (-Delta)(alpha /2) + V , where V belongs to higher -order Kato class.