Lie Groups and Representation Theory

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Date, time & place Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.)

2013/12/17

16:30-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Koichi Kaizuka (University of Tsukuba)
A characterization of the $L^{2}$-range of the
Poisson transform on symmetric spaces of noncompact type (JAPANESE)
[ Abstract ]
Characterizations of the joint eigenspaces of invariant
differential operators in terms of the Poisson transform have been one of the central problems in harmonic analysis on symmetric spaces.
From the point of view of spectral theory, Strichartz (J. Funct.
Anal.(1989)) formulated a conjecture concerning a certain image
characterization of the Poisson transform of the $L^{2}$-space on the boundary on symmetric spaces of noncompact type. In this talk, we employ techniques in scattering theory to present a positive answer to the Strichartz conjecture.