Abstract
The main purpose of this paper is to solve Strichartz conjecture concerning an image characterization of the Poisson transform in the L2-theory on symmetric spaces of noncompact type. We prove that the Poisson transform provides an isomorphism between the L2-space on the boundary and a certain weighted L2-space consisting of joint eigenfunctions on symmetric spaces of noncompact type. Our approach is based on the scattering theory for the Schrödinger operator. Moreover, we give a Fourier restriction estimate and an asymptotic formula for the Poisson transform.
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