# Resolvents and complex powers of semiclassical cone operators

@article{Hintz2020ResolventsAC, title={Resolvents and complex powers of semiclassical cone operators}, author={P. Hintz}, journal={arXiv: Analysis of PDEs}, year={2020} }

We give a uniform description of resolvents and complex powers of elliptic semiclassical cone differential operators as the semiclassical parameter $h$ tends to $0$. An example of such an operator is the shifted semiclassical Laplacian $h^2\Delta_g+1$ on a manifold $(X, g)$ of dimension $n\geq 3$ 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 conormalâ€¦Â Expand

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