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Unitary representations of Lie groups and Gårding's inequality

Authors: Ola Bratteli, Fred Goodman, Palle Jorgensen and Derek W. Robinson
Journal: Proc. Amer. Math. Soc. 107 (1989), 627-632
MSC: Primary 22E45; Secondary 35J99
MathSciNet review: 947312
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Abstract: We prove two versions of Gåding's inequality for strongly elliptic operators in the enveloping Lie algebra associated with a unitary representation of a Lie group. We then deduce a characterization of the differential structure of the representation in terms of the elliptic operators.

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

  • [G] Roe W. Goodman, One-parameter groups generated by operators in an enveloping algebra., J. Functional Analysis 6 (1970), 218–236. MR 0268330
  • [L1] R. P. Langlands, Some holomorphic semi-groups, Proc. Nat. Acad. Sci. U.S.A. 46 (1960), 361–363. MR 0177303
  • [L2] -, Semigroups and representations of Lie groups, Yale University thesis, 1960.
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  • [R2] -, The analytic structure of representations of Lie groups (in preparation).

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Article copyright: © Copyright 1989 American Mathematical Society

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