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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the boundedness and unboundedness of certain convolution operators on nilpotent Lie groups

Author: Roe Goodman
Journal: Proc. Amer. Math. Soc. 39 (1973), 409-413
MSC: Primary 22E30
MathSciNet review: 0320227
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Abstract: One method of proving irreducibility of the ``principal series'' representations of semisimple Lie groups involves showing that a certain nonintegrable function on a nilpotent subgroup $ X$ cannot be regularized to give a bounded convolution operator on $ {L_2}(X)$. This note gives an elementary proof of this unboundedness property for the groups $ X$ which occur in real-rank one semisimple groups.

References [Enhancements On Off] (What's this?)

  • [1] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, 2nd ed., Cambridge Univ. Press, New York, 1952. MR 13, 727. MR 0046395 (13:727e)
  • [2] A. W. Knapp and E. M. Stein, Intertwining operators for semi-simple groups, Ann. of Math. (2) 93 (1971), 489-578. MR 0460543 (57:536)

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Article copyright: © Copyright 1973 American Mathematical Society

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