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The aim of this article is twofold. First, we study the uniform complex time heat kernel estimates ofe−z(−Δ)α2{e}^{-z{\left(-\Delta )}^{\frac{\alpha }{2}}}forα&gt;0,z∈C+\alpha \gt 0,z\in {{\mathbb{C}}}^{+}. To this end, we establish the asymptotic estimates forP(z,x)P\left(z,x)withzzsatisfying0&lt;ω≤∣θ∣&lt;π20\lt \omega \le | \theta | \lt \frac{\pi }{2}followed by the uniform complex time heat kernel estimates. Second, we studied the uniform complex time estimates of the analytic semigroup generated byH=(−Δ)α2+VH={\left(-\Delta )}^{\tfrac{\alpha }{2}}+V, whereVVbelongs to higher-order Kato class.

Uniform complex time heat Kernel estimates without Gaussian bounds