Radon transforms on homogeneous spaces and their application to harmonic analysis

点击翻译按钮获取中文摘要

We studied Radon transforms on homogeneous spaces, and their applications to harmonic analysis. Our results are as follows. (1) We proved that the ranges of generalized matrix Radon transforms are characterized by Pfaffian type invariant differential operators. In addition, we also obtained the inversion formulas. (2) We proved that under some condition the support of the fundamental solution to the Schroedinger equation on a compact symmetric space becomes a lower dimensional subset at a rational time and that it coincides with the whole symmetric space at an irrational time.