Spectral and Scattering Theory for the Laplacian on Asymptotically Euclidian Spaces
By R. Melrose. Spectral and scattering theory, 2020
188 citations recorded by the source corpus.
There are many approaches to conventional Euclidian scattering theory. In this exposition an essentially microlocal view is adopted. Apart from its intrinsic interest this is intended as preparation for later generalization, to more complicated geometric settings. In fact, the treatment given here extends beyond the usual confines of scattering theory in that the spectral and scattering theory, at least the elementary part, is covered for the Laplacian associated to a ‘scattering metric’ on any compact manifold with boundary. By a scattering metric on a compact manifold with boundary,X, we shall mean a Riemann metric on the interior of X which can be brought to the form
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c27c2c4165900dcdc9ce921806d4c71378ff7fb6
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In Applied Mathematics
- Plamen Stefanov
- Gunther Uhlmann
- András Vasy
- Mikko Salo
- Venkateswaran P. Krishnan
- Gang Bao
- C. Guillarmou
- Hai E Zhang
In Computational Theory and Mathematics
- Gunther Uhlmann
- Plamen Stefanov
- András Vasy
- Mikko Salo
- Venkateswaran P. Krishnan
- Katya Krupchyk
- Matti Lassas
- Guillaume Bal
In Mathematical Physics
- Gunther Uhlmann
- Plamen Stefanov
- András Vasy
- Mikko Salo
- Gang Bao
- Hai E Zhang
- Matti Lassas
- Venkateswaran P. Krishnan
Citations in the corpus
- Inverting the local geodesic X-ray transform on tensors (2014, background): “Since it plays a crucial role even in the setup, by giving the bundles of which our tensors are sections of, as well as the gauge condition, we need to discuss scattering geometry and the scattering pseudodifferential algebra, introduced by Melrose in [12], at least briefly.”
- Local and global boundary rigidity and the geodesic X-ray transform in the normal gauge (2017, background): “More precisely then, the pseudodifferential operator class is that of scattering pseudodifferential operators, introduced by Melrose in [15] in this generality, but having precedents in R in the works of Parenti and Shubin [19, 22], and in this case it is also a special case of Hörmander’s Weyl calc”