2020/10/04 by Peter Hintz, Hintz, Peter · 4 citations
Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Analysis and Transform Methods #Medical Imaging Techniques and Applications
paper · pdf · doi:10.48550/arxiv.2010.01593
openalex publication_date 2020/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 h2Δg+1 on a manifold (X, g) of dimension n≥ 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 conormal distributions on a suitable resolution of the space [0,1)h× X× X of h-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 (h2Δg+1)w/2 for Re w∈(-(n)/(2),(n)/(2)) and use this to prove the propagation of semiclassical regularity through a cone point on a range of weighted semiclassical function spaces.