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The subalgebra of $L\sp 1(AN)$ generated by the Laplacian

1993
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Proceedings of the American Mathematical Society
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We prove that for the Iwasawa AN groups corresponding to complex semisimple Lie groups, the subalgebra of L[{AN) associated to a distinguished laplacian is isomorphic with the algebra of integrable radial functions on R" . In [1] Cowling et al. derived a formula for the heat semigroup generated by a distinguished laplacian on a large class of Iwasawa AN groups and proved that the maximal function constructed from the semigroup is of weak type (1, 1). In this paper we show that in the case of

doi:10.1090/s0002-9939-1993-1111218-3
fatcat:nkomrvw37zat3pzutierb644s4