For α∈(0,2) and M0, we consider a family of nonlocal operators {Δ+aαΔα/2,a∈(0,M]} on Rd under Kato class gradient perturbation. We establish the existence and uniqueness of their fundamental solutions, and derive their sharp two-sided estimates. The estimates give explicit dependence on...

We prove the existence of the integrated density of states for subordinate Brownian motions in the presence of the Poissonian random potentials on the Sierpiński gasket.