Resolvents and complex powers of semiclassical cone operators

We give a uniform description of resolvents and complex powers elliptic semiclassical cone differential operators as the parameter h tends to 0. An example such an operator is shifted Laplacian 2 ? g + 1 $h^2\Delta _g+1$ on manifold ( X , ) $(X,g)$ dimension n ? 3 $n\ge 3$ with conic singularities. Our approach constructive based techniques from geometric microlocal analysis: we construct Schwartz kernels conormal distributions suitable resolution space [ 0 × $[0,1)_h\times X\times X$ h-dependent integral kernels; construction relies calculus second parameter. As application, characterize domains w / ${\big (h^2\Delta _g+1\big )}^{w/2}$ for Re ? ? $\operatorname{Re}w\in \left(-\tfrac{n}{2},\tfrac{n}{2}\right)$ use this prove propagation regularity through point range weighted function spaces.