Journal article
The heat semigroup and integrability of Lie algebras
Journal of functional analysis, Vol.79(2), pp.351-397
1988
DOI: 10.1016/0022-1236(88)90018-3
Abstract
Let (∥dU(x 1 S t ∥⩽c/t 1 2 , 0 < ⩽ 1) denote a continuous representation U of a Lie group G acting on a Banach space B and S the semigroup generated by the closed Laplacian associated with a basis of the Lie algebra g in the derived representation dU . We prove there is a c > 0 such that ∥dU(x i ) S t ∥ ⩽ c t 1 2 , 0 < t ⩽ 1 , for all x i in the basis of g , and we also prove that this property is characteristic for integrability of a Lie algebra of operators satisfying the usual dissipativity requirements for generators of one-parameter groups. The basic estimate is established from bounds on the heat kernel associated with S.
Details
- Title: Subtitle
- The heat semigroup and integrability of Lie algebras
- Creators
- Ola BratteliFrederick M GoodmanPalle E.T JørgensenDerek W Robinson
- Resource Type
- Journal article
- Publication Details
- Journal of functional analysis, Vol.79(2), pp.351-397
- DOI
- 10.1016/0022-1236(88)90018-3
- ISSN
- 1096-0783
- eISSN
- 1096-0783
- Language
- English
- Date published
- 1988
- Academic Unit
- Mathematics
- Record Identifier
- 9983985813202771
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