By combining some results of C. S. Herz on the Fourier algebra with the notion of contractions of Lie groups, we prove theorems which allow transference of multipliers either from the Lie algebra or from the Cartan motion group associated to a compact Lie group to the group itself.
We study a method of approximating representations of the group by those of the group . As a consequence we establish a version of a theorem of DeLeeuw for Fourier multipliers of that applies to the “restrictions” of a function on the dual of to the dual of .
We study the relative discrete series of the -space of the sections of a line bundle over a bounded symmetric domain. We prove that all the discrete series appear as irreducible submodules of the tensor product of a holomorphic discrete series with a finite dimensional representation.
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