Beschreibung:
<jats:title>Abstract</jats:title><jats:p>We give a uniform description of resolvents and complex powers of elliptic semiclassical cone differential operators as the semiclassical parameter <jats:italic>h</jats:italic> tends to 0. An example of such an operator is the shifted semiclassical Laplacian on a manifold of dimension with conic singularities. Our approach is constructive and based on techniques from geometric microlocal analysis: we construct the Schwartz kernels of resolvents and complex powers as conormal distributions on a suitable resolution of the space of <jats:italic>h</jats:italic>‐dependent integral kernels; the construction of complex powers relies on a calculus with a second semiclassical parameter. As an application, we characterize the domains of for and use this to prove the propagation of semiclassical regularity through a cone point on a range of weighted semiclassical function spaces.</jats:p>