A note on the L2-harmonic analysis of the Joint-Eigenspace Fourier transform
Abstract
We consider the irreducibility of the regular representation of a noncompact semisimpe Lie group G on the Hilbert space of the image of the Joint-Eigenspace Fourier transform on its corresponding symmetric space G/K. The L2-decomposition of the Joint-Eigenspace Fourier transform leads to the complete characterization of the said irreducibility in terms of the simplicity of a pair of members of a*C.
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