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Author
Date
2022-10Type
- Journal Article
ETH Bibliography
yes
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Abstract
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 h2 Δg + 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 (h2 Δg + 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. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000577283Publication status
publishedExternal links
Journal / series
Mathematische NachrichtenVolume
Pages / Article No.
Publisher
Wiley-VCHSubject
conic singularities; semiclassical cone operators; pseudodifferential calculus; complex powers; propagation of singularitiesOrganisational unit
09749 - Hintz, Peter / Hintz, Peter
09749 - Hintz, Peter / Hintz, Peter
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ETH Bibliography
yes
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