Geodesic
A Characterization of the L2-Range of the Poisson Transform with Real and Singular Spectral Parameter on Symmetric Spaces of Noncompact Type
Koichi Kaizuka1, 2
1Department of Mathematics, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588, Japan
2Dept. of Mathematics, Nippon Medical School, 1-7-1 Kyounan-cho, Musashino-shi, Tokyo 180-0023, Japan
Journal of Lie Theory, Tome 28 (2018) no. 2, pp. 581-607

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 43A85, 22E30, 43A90
Mots-clés : Symmetric space, Poisson transform, joint eigenfunction, scattering theory

Koichi Kaizuka  1 , 2

1 Department of Mathematics, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588, Japan
2 Dept. of Mathematics, Nippon Medical School, 1-7-1 Kyounan-cho, Musashino-shi, Tokyo 180-0023, Japan 
Koichi Kaizuka. A Characterization of the L2-Range of the Poisson Transform with Real and Singular Spectral Parameter on Symmetric Spaces of Noncompact Type. Journal of Lie Theory, Tome 28 (2018) no. 2, pp. 581-607. http://geodesic.mathdoc.fr/item/JOLT_2018_28_2_a12/
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     author = {Koichi Kaizuka},
     title = {A {Characterization} of the {L\protect\textsuperscript{2}-Range} of the {Poisson} {Transform} with {Real} and {Singular} {Spectral} {Parameter} on {Symmetric} {Spaces} of {Noncompact} {Type}},
     journal = {Journal of Lie Theory},
     pages = {581--607},
     year = {2018},
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