The Klein-Gordon equation on asymptotically flat spacetimes
By Dean Baskin
On the Radon-Carleman problem in uniformly rectifiable domains
By Irina Mitrea
Appears in collection : Avancées récentes en analyse géométrique / Recent advances in geometric analysis
We study the spectrum of a fractional Laplacian equation with drift in suitable weighted spaces. This operator arises when studying the fractional heat equation in self-similar variables. We show, in the radially symmetric case, compactness, and then calculate the eigenfunctions in terms of Laguerre polynomials. The proofs involve conformal geometry, Mellin transform and complex analysis methods.