2008/08/08 by Koichi Kaizuka, Kaizuka, Koichi
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Mathematical Analysis and Transform Methods #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.0808.1191
In this article we prove time-global smoothing effects of dispersive pseudodifferential equations with constant coefficient radially symmetric symbols on real rank one symmetric spaces of noncompact type. We also discuss gain of regularities according to decay rates of initial values for the Schroedinger evolution equation. We introduce some isometric operators and reduce the arguments to the well-known Euclidean case. In our proof, Helgason's Fourier transform and the Radon transform as an elliptic Fourier integral operator play crucial roles.