Abstract
Let M be a smooth manifold, \({I\subset M}\) a closed embedded submanifold of M and U an open subset of M. In this paper, we find conditions using a geometric notion of scaling for \({t\in \mathcal{D}^{\prime}(U{\setminus} I)}\) to admit an extension in \({\mathcal{D}^\prime(U)}\). We give microlocal conditions on t which allow to control the wave front set of the extension generalizing a previous result of Brunetti–Fredenhagen. Furthermore, we show that there is a subspace of extendible distributions for which the wave front of the extension is minimal which has applications for the renormalization of quantum field theory on curved spacetimes.
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Communicated by Christoph Kopper.
This work was supported in part by the Labex CEMPI (ANR-11-LABX-0007-01).
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Dang, N.V. The Extension of Distributions on Manifolds, a Microlocal Approach. Ann. Henri Poincaré 17, 819–859 (2016). https://doi.org/10.1007/s00023-015-0419-8
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DOI: https://doi.org/10.1007/s00023-015-0419-8