Search results for "Wave front set"
showing 2 items of 2 documents
Linearized Calderón problem and exponentially accurate quasimodes for analytic manifolds
2022
In this article we study the linearized anisotropic Calderon problem on a compact Riemannian manifold with boundary. This problem amounts to showing that products of pairs of harmonic functions of the manifold form a complete set. We assume that the manifold is transversally anisotropic and that the transversal manifold is real analytic and satisfies a geometric condition related to the geometry of pairs of intersecting geodesics. In this case, we solve the linearized anisotropic Calderon problem. The geometric condition does not involve the injectivity of the geodesic X-ray transform. Crucial ingredients in the proof of our result are the construction of Gaussian beam quasimodes on the tra…
Pseudodifferential operators of Beurling type and the wave front set
2008
AbstractWe investigate the action of pseudodifferential operators of Beurling type on the wave front sets. More precisely, we show that these operators are microlocal, that is, preserve or reduce wave front sets. Some consequences on micro-hypoellipticity are derived.