Unitary representations of Lie groups and Gårding’s inequality
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- by Ola Bratteli, Fred Goodman, Palle Jorgensen and Derek W. Robinson PDF
- Proc. Amer. Math. Soc. 107 (1989), 627-632 Request permission
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
- Roe W. Goodman, One-parameter groups generated by operators in an enveloping algebra. , J. Functional Analysis 6 (1970), 218–236. MR 0268330, DOI 10.1016/0022-1236(70)90059-5
- R. P. Langlands, Some holomorphic semi-groups, Proc. Nat. Acad. Sci. U.S.A. 46 (1960), 361–363. MR 177303, DOI 10.1073/pnas.46.3.361 —, Semigroups and representations of Lie groups, Yale University thesis, 1960.
- Derek W. Robinson, The differential and integral structure of representations of Lie groups, J. Operator Theory 19 (1988), no. 1, 95–128. MR 950828 —, The analytic structure of representations of Lie groups (in preparation).
Additional Information
- © Copyright 1989 American Mathematical Society
- 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