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Journal of Lie Theory 28 (2018), No. 2, 581--607
Copyright Heldermann Verlag 2018

A Characterization of the L2-Range of the Poisson Transform with Real and Singular Spectral Parameter on Symmetric Spaces of Noncompact Type

Koichi Kaizuka
Department of Mathematics, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588, Japan
and: Dept. of Mathematics, Nippon Medical School, 1-7-1 Kyounan-cho, Musashino-shi, Tokyo 180-0023, Japan

In a previous work we proved the Strichartz conjecture concerning an image characterization of the Poisson transform with real and regular spectral parameter. In this paper, by developing weighted L2-estimates on symmetric spaces of noncompact type, we extend our previous result to the case of real and singular spectral parameter. In the real and singular case, a certain degeneracy appears in the scattering formula for the Poisson transform.

Keywords: Symmetric space, Poisson transform, joint eigenfunction, scattering theory.

MSC: 43A85; 22E30, 43A90

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