Unitary representations of unimodular Lie groups in Bergman spaces
β Scribed by Giuseppe Della Sala, Joe J. Perez
- Book ID
- 118780575
- Publisher
- Springer-Verlag
- Year
- 2011
- Tongue
- French
- Weight
- 262 KB
- Volume
- 272
- Category
- Article
- ISSN
- 0025-5874
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π SIMILAR VOLUMES
We consider the following class of unitary representations ? of some (real) Lie group G which has a matched pair of symmetries described as follows: (i) Suppose G has a period-2 automorphism {, and that the Hilbert space H(?) carries a unitary operator J such that J?=(? b {) J (i.e., selfsimilarity)
We show that in the presence of suitable commutator estimates, a projective unitary representation of the Lie algebra of a connected and simply connected Lie group G exponentiates to G. Our proof does not assume G to be finite-dimensional or of Banach Lie type and therefore encompasses the diffeomor