A characterization of the L²-range of the Poisson transform related to Strichartz conjecture on symmetric spaces of noncompact type

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• 作者：Koichi Kaizuka ^{kaizuka@math.gakushuin.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 43A85 ; secondary ; 35P25 ; 43A90 ; 58J50
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：5 November 2016
• 年：2016
• 卷：303
• 期：Complete
• 页码：464-501
• 全文大小：597 K

文摘

The main purpose of this paper is to solve Strichartz conjecture concerning an image characterization of the Poisson transform in the L²$L^2$-theory on symmetric spaces of noncompact type. We prove that the Poisson transform provides an isomorphism between the L²$L^2$-space on the boundary and a certain weighted L²$L^2$-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.