Geodesic
Decomposition of boundary representations on the Lobachevsky plane associated with linear bundles
Vestnik rossijskih universitetov. Matematika, Tome 24 (2019) no. 128, pp. 368-375

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Earlier we described canonical (labelled by $\lambda\in \Bbb C$) and accompanying boundary representations of the group $G={\rm {SU}} \, (1,1)$ on the Lobachevsky plane $D$ in sections of linear bundles and decomposed canonical representations into irreducible ones. Now we decompose representations acting on distributions concentrated at the boundary of $D$. In the generic case $2\lambda\notin \Bbb N$ they are diagonalizable, in the exceptional case Jordan blocks appear.
Keywords: Lobachevsky plane; canonical representations; distributions; boundary representations; Poisson transforms. 
@article{VTAMU_2019_24_128_a2,
     author = {L. I. Grosheva},
     title = {Decomposition of boundary representations on the {Lobachevsky} plane  associated with linear bundles},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {368--375},
     publisher = {mathdoc},
     volume = {24},
     number = {128},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2019_24_128_a2/}
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L. I. Grosheva. Decomposition of boundary representations on the Lobachevsky plane  associated with linear bundles. Vestnik rossijskih universitetov. Matematika, Tome 24 (2019) no. 128, pp. 368-375. http://geodesic.mathdoc.fr/item/VTAMU_2019_24_128_a2/