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Proceedings of the American Mathematical Society

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

 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1989-0947312-6
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.
  • [R1] Derek W. Robinson, The differential and integral structure of representations of Lie groups, J. Operator Theory 19 (1988), no. 1, 95–128. MR 950828
  • [R2] -, The analytic structure of representations of Lie groups (in preparation).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0947312-6
Article copyright: © Copyright 1989 American Mathematical Society