Smoothing effects of dispersive equations on real rank one symmetric spaces

Details Smoothing effects of dispersive equations on real rank one symmetric spaces Smoothing effects of dispersive equations on real rank one symmetric spaces

2008-08-08

arxiv.org/abs/0808.1191v2

Mathematics

Analysis of PDEs

25 pages, 3 figures

Scientific paper

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.

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