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Boundary behavior of limits of discrete series representations of real rank one semisimple groups

Boundary behavior of limits of discrete series representations of real rank one semisimple groups

The decomposition of the reducible unitary principal series of a connected semisimple Lie group having real rank one and a simply connected complexif ication is exhibited on a global analytic level in such a way that it is seen to correspond to a phenomenon in classical Fourier analysis, this is …